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<blockquote data-quote="MaD-DoC" data-source="post: 2312713" data-attributes="member: 56284">700 is the number of symmetric 8-cubes. &nbsp; &nbsp;&nbsp; 701 = 10 + 21 + 32 + 43 + 54. &nbsp; &nbsp;&nbsp; 702 ??? &nbsp; &nbsp;&nbsp; 703 is a Kaprekar number. &nbsp; &nbsp;&nbsp; 704 is the number of sided octominoes. &nbsp; &nbsp;&nbsp; 705 is the smallest Lucas pseudoprime. &nbsp; &nbsp;&nbsp; 706 ??? &nbsp; &nbsp;&nbsp; 707 is the smallest number whose reciprocal has period 12. &nbsp; &nbsp;&nbsp; 708 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps. &nbsp; &nbsp;&nbsp; 709 is the number of connected planar graphs with 9 edges. &nbsp; &nbsp;&nbsp; 710 is the number of connected graphs with 9 edges. &nbsp; &nbsp;&nbsp; 711 ??? &nbsp; &nbsp;&nbsp; 712 is the largest number known that does not have any digits in common with its 8th power. &nbsp; &nbsp;&nbsp; 713 is the number of commutative monoids of order 7 with 4 idempotents. &nbsp; &nbsp;&nbsp; 714 is the smallest number which has equal numbers of every digit in bases 2 and 5. &nbsp; &nbsp;&nbsp; 715 = 13C4. &nbsp; &nbsp;&nbsp; 716 is the smallest number whose cube contains four 6's. &nbsp; &nbsp;&nbsp; 717 is a palindrome in base 2 and in base 10. &nbsp; &nbsp;&nbsp; 718 is the number of unlabeled topologies with 6 elements. &nbsp; &nbsp;&nbsp; 719 is the number of rooted trees with 10 vertices. &nbsp; &nbsp;&nbsp; 720 = 6! &nbsp; &nbsp;&nbsp; 721 is the smallest number which can be written as the difference of 2 cubes in 2 ways. &nbsp; &nbsp;&nbsp; 722 is the sum of the 4th powers of the first 3 primes. &nbsp; &nbsp;&nbsp; 723 ??? &nbsp; &nbsp;&nbsp; 724 is the number of different arrangements of 10 non-attacking queens on an 10×10 chessboard. &nbsp; &nbsp;&nbsp; 725 ??? &nbsp; &nbsp;&nbsp; 726 is a pentagonal pyramidal number. &nbsp; &nbsp;&nbsp; 727 has the property that its square is the concatenation of two consecutive numbers. &nbsp; &nbsp;&nbsp; 728 is the smallest number n where n and n+1 are both products of 5 or more primes. &nbsp; &nbsp;&nbsp; 729 = 36. &nbsp; &nbsp;&nbsp; 730 is the number of connected bipartite graphs with 9 vertices. &nbsp; &nbsp;&nbsp; 731 is the number of planar partitions of 14. &nbsp; &nbsp;&nbsp; 732 = 17 + 26 + 35 + 44 + 53 + 62 + 71. &nbsp; &nbsp;&nbsp; 733 is the sum of the digits of 444. &nbsp; &nbsp;&nbsp; 734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways. &nbsp; &nbsp;&nbsp; 735 is the smallest number that is the concatenation of its distinct prime factors. &nbsp; &nbsp;&nbsp; 736 is a strong Friedman number. &nbsp; &nbsp;&nbsp; 737 ??? &nbsp; &nbsp;&nbsp; 738 = 6 + 66 + 666. &nbsp; &nbsp;&nbsp; 739 has a base 2 representation that begins with its base 9 representation. &nbsp; &nbsp;&nbsp; 740 is the number of self-avoiding walks of length 8. &nbsp; &nbsp;&nbsp; 741 is the number of multigraphs with 6 vertices and 8 edges. &nbsp; &nbsp;&nbsp; 742 is the smallest number that is one more than triple its reverse. &nbsp; &nbsp;&nbsp; 743 is the number of independent sets of the graph of the 4-dimensional hypercube. &nbsp; &nbsp;&nbsp; 744 is the number of perfect squared rectangles of order 14. &nbsp; &nbsp;&nbsp; 745 is the smallest number whose square begins with three 5's. &nbsp; &nbsp;&nbsp; 746 = 17 + 24 + 36. &nbsp; &nbsp;&nbsp; 747 ??? &nbsp; &nbsp;&nbsp; 748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner. &nbsp; &nbsp;&nbsp; 749 is the number of ways to divide a 7×7 grid of points into two sets using a straight line. &nbsp; &nbsp;&nbsp; 750 is the Stirling number of the second kind S(10,. &nbsp; &nbsp;&nbsp; 751 is the index of a prime Woodall number. &nbsp; &nbsp;&nbsp; 752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube. &nbsp; &nbsp;&nbsp; 753 is the smallest number whose cube contains 4 consecutive 7's. &nbsp; &nbsp;&nbsp; 754 ??? &nbsp; &nbsp;&nbsp; 755 is the number of trees on 14 vertices with diameter 6. &nbsp; &nbsp;&nbsp; 756 is the maximum number of regions space can be divided into by 14 spheres. &nbsp; &nbsp;&nbsp; 757 is the smallest number whose reciprocal has a period of 27. &nbsp; &nbsp;&nbsp; 758 ??? &nbsp; &nbsp;&nbsp; 759 ??? &nbsp; &nbsp;&nbsp; 760 is the number of partitions of 37 into distinct parts. &nbsp; &nbsp;&nbsp; 761 ??? &nbsp; &nbsp;&nbsp; 762 is the starting location of 999999 in the decimal expansion of π. &nbsp; &nbsp;&nbsp; 763 is the smallest number whose 4th power contains every digit at least once. &nbsp; &nbsp;&nbsp; 764 is the number of 8×8 symmetric permutation matrices. &nbsp; &nbsp;&nbsp; 765 is a Kaprekar constant in base 2. &nbsp; &nbsp;&nbsp; 766 is the number of series-reduced planted trees with 9 leaves. &nbsp; &nbsp;&nbsp; 767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution. &nbsp; &nbsp;&nbsp; 768 is the number of subsets of {1,2,3,...,12} that have an integer average. &nbsp; &nbsp;&nbsp; 769 is the total number of digits of all binary numbers of length 1-7. &nbsp; &nbsp;&nbsp; 770 is the number of digits of the 15th perfect number. &nbsp; &nbsp;&nbsp; 771 is the number of intersections when all the diagonals of a regular 14-gon are drawn. &nbsp; &nbsp;&nbsp; 772 ??? &nbsp; &nbsp;&nbsp; 773 is the smallest odd number n so that n+2k is composite for all k&lt;n. &nbsp; &nbsp;&nbsp; 774 ??? &nbsp; &nbsp;&nbsp; 775 is the smallest number whose 9th power has 26 digits. &nbsp; &nbsp;&nbsp; 776 ??? &nbsp; &nbsp;&nbsp; 777 is a repdigit in base 6 and in base 10. &nbsp; &nbsp;&nbsp; 778 is the number of ways a 5×1 rectangle can be surrounded by 5×1 rectangles. &nbsp; &nbsp;&nbsp; 779 ??? &nbsp; &nbsp;&nbsp; 780 = (5+7) × (5+× (5+0). &nbsp; &nbsp;&nbsp; 781 = 11111 in base 5. &nbsp; &nbsp;&nbsp; 782 is a number whose sum of divisors is a 4th power. &nbsp; &nbsp;&nbsp; 783 is the number of 11-ominoes that tile the plane by translation. &nbsp; &nbsp;&nbsp; 784 is the sum of the first 7 cubes. &nbsp; &nbsp;&nbsp; 785 are the last 3 digits of the sum of the first 785 squares. &nbsp; &nbsp;&nbsp; 786 is the largest known n for which 2nCn is not divisible by the square of an odd prime. &nbsp; &nbsp;&nbsp; 787 is a palindrome in base 3 and in base 10. &nbsp; &nbsp;&nbsp; 788 is the smallest of 6 consecutive numbers divisible by 6 consecutive primes. &nbsp; &nbsp;&nbsp; 789 are the first 3 digits of 9789. &nbsp; &nbsp;&nbsp; 790 ??? &nbsp; &nbsp;&nbsp; 791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12. &nbsp; &nbsp;&nbsp; 792 is the number of partitions of 21. &nbsp; &nbsp;&nbsp; 793 is one less than twice its reverse. &nbsp; &nbsp;&nbsp; 794 = 16 + 26 + 36. &nbsp; &nbsp;&nbsp; 795 is a number whose sum of divisors is a 4th power. &nbsp; &nbsp;&nbsp; 796 ??? &nbsp; &nbsp;&nbsp; 797 is the number of functional graphs on 9 vertices. &nbsp; &nbsp;&nbsp; 798 is the number of ternary square-free words of length 16. &nbsp; &nbsp;&nbsp; 799 is the smallest number whose sum of digits is composite and whose sum of digits cubed is prime. &nbsp; &nbsp;&nbsp; 800 = 2222 in base 7. &nbsp; &nbsp;&nbsp; 801 = (7! + 8! + 9! + 10!) / (7 × 8 × 9 × 10). &nbsp; &nbsp;&nbsp; 802 is the number of isomers of C13H28. &nbsp; &nbsp;&nbsp; 803 is a value of n for which σ<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down&nbsp; &nbsp; (n)" loading="lazy" data-shortname="(n)" /> is a repdigit. &nbsp; &nbsp;&nbsp; 804 is a value of n for which 2φ<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down&nbsp; &nbsp; (n)" loading="lazy" data-shortname="(n)" /> = φ(n+1). &nbsp; &nbsp;&nbsp; 805 is the number of possible positions in Checkers after 4 moves. &nbsp; &nbsp;&nbsp; 806 is not the sum of a square, a cube, a 4th power, and a 5th power. &nbsp; &nbsp;&nbsp; 807 ??? &nbsp; &nbsp;&nbsp; 808 is a strobogrammatic number. &nbsp; &nbsp;&nbsp; 809 is a member of the Fibonacci-type sequence starting with 1 and 5. &nbsp; &nbsp;&nbsp; 810 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1. &nbsp; &nbsp;&nbsp; 811 ??? &nbsp; &nbsp;&nbsp; 812 is the number of triangles of any size contained in the triangle of side 14 on a triangular grid. &nbsp; &nbsp;&nbsp; 813 are the first 3 digits of 813e. &nbsp; &nbsp;&nbsp; 814 is a value of n so that n(n+5) is a palindrome. &nbsp; &nbsp;&nbsp; 815 is a Lucas 3-step number. &nbsp; &nbsp;&nbsp; 816 = 18C3. &nbsp; &nbsp;&nbsp; 817 ??? &nbsp; &nbsp;&nbsp; 818 is the number of ways to dissect a 12-gon using non-crossing diagonals into polygons with an even number of sides. &nbsp; &nbsp;&nbsp; 819 is the smallest number so that it and its successor are both the product of 2 primes and the square of a prime. &nbsp; &nbsp;&nbsp; 820 = 1111 in base 9. &nbsp; &nbsp;&nbsp; 821 is a number n for which n, n+2, n+6, and n+8 are all prime. &nbsp; &nbsp;&nbsp; 822 is the number of planar graphs with 7 vertices. &nbsp; &nbsp;&nbsp; 823 is a number that does not have any digits in common with its cube. &nbsp; &nbsp;&nbsp; 824 ??? &nbsp; &nbsp;&nbsp; 825 is the number of ways to legally add 2 sets of parentheses to a product of 9 variables. &nbsp; &nbsp;&nbsp; 826 ??? &nbsp; &nbsp;&nbsp; 827 is the number of asymmetric trees with 11 vertices. &nbsp; &nbsp;&nbsp; 828 ??? &nbsp; &nbsp;&nbsp; 829 is a value of n for which π<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down&nbsp; &nbsp; (n)" loading="lazy" data-shortname="(n)" /> is the product of the digits of n. &nbsp; &nbsp;&nbsp; 830 ??? &nbsp; &nbsp;&nbsp; 831 is the number of monic polynomials of degree 9 with integer coefficients whose complex roots are all in the unit disk. &nbsp; &nbsp;&nbsp; 832 is the maximum number of pieces a torus can be cut into with 16 cuts. &nbsp; &nbsp;&nbsp; 833 is a centered octahedral number. &nbsp; &nbsp;&nbsp; 834 is the maximum number of regions a cube can be cut into with 17 cuts. &nbsp; &nbsp;&nbsp; 835 is the 9th Motzkin number. &nbsp; &nbsp;&nbsp; 836 is a non-palindrome with a palindromic square. &nbsp; &nbsp;&nbsp; 837 ??? &nbsp; &nbsp;&nbsp; 838 ??? &nbsp; &nbsp;&nbsp; 839 has a base 5 representation that begins with its base 9 representation. &nbsp; &nbsp;&nbsp; 840 is the smallest number divisble by 1 through 8. &nbsp; &nbsp;&nbsp; 841 is a square that is also the sum of 2 consecutive squares. &nbsp; &nbsp;&nbsp; 842 is the ratio of Fibonacci numbers. &nbsp; &nbsp;&nbsp; 843 is the 14th Lucas number. &nbsp; &nbsp;&nbsp; 844 is the smallest number so that it and the next four numbers are squareful numbers. &nbsp; &nbsp;&nbsp; 845 ??? &nbsp; &nbsp;&nbsp; 846 has the property that its square is the concatenation of two consecutive numbers. &nbsp; &nbsp;&nbsp; 847 is the sum of the digits of the 14th Mersenne prime. &nbsp; &nbsp;&nbsp; 848 is the number of inequivalent binary linear codes of length 9. &nbsp; &nbsp;&nbsp; 849 is a value of n for which σ(n-1) = σ(n+1). &nbsp; &nbsp;&nbsp; 850 is the number of trees on 14 vertices with diameter 7. &nbsp; &nbsp;&nbsp; 851 is the number of ordered partitions of 18 into distinct parts. &nbsp; &nbsp;&nbsp; 852 is the number of 6-colorable connected graphs with 7 vertices. &nbsp; &nbsp;&nbsp; 853 is the number of connected graphs with 7 vertices. &nbsp; &nbsp;&nbsp; 854 has the property that it and its square together use the digits 1-9 once. &nbsp; &nbsp;&nbsp; 855 is the smallest number which is the sum of 5 consecutive squares or 2 consecutive cubes. &nbsp; &nbsp;&nbsp; 856 is a member of the Fibonacci-type sequence starting with 1 and 9. &nbsp; &nbsp;&nbsp; 857 is a value of n for which φ<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down&nbsp; &nbsp; (n)" loading="lazy" data-shortname="(n)" /> = φ(n-1) + φ(n-2). &nbsp; &nbsp;&nbsp; 858 is the smallest palindrome with 4 different prime factors. &nbsp; &nbsp;&nbsp; 859 is the number of planar partitions of 11. &nbsp; &nbsp;&nbsp; 860 ??? &nbsp; &nbsp;&nbsp; 861 = 7 + 77 + 777. &nbsp; &nbsp;&nbsp; 862 is a number whose sum of divisors is a 4th power. &nbsp; &nbsp;&nbsp; 863 is a value of n so that n(n+6) is a palindrome. &nbsp; &nbsp;&nbsp; 864 is the number of partitions of 38 into distinct parts. &nbsp; &nbsp;&nbsp; 865 ??? &nbsp; &nbsp;&nbsp; 866 is the number of sided 10-iamonds. &nbsp; &nbsp;&nbsp; 867 is the number of graphs with 8 vertices that have chromatic number 5. &nbsp; &nbsp;&nbsp; 868 has a square root whose decimal part starts with the digits 1-9 in some order. &nbsp; &nbsp;&nbsp; 869 is the number of different resistances that can be created in a circuit of 9 equal resistors. &nbsp; &nbsp;&nbsp; 870 is the sum of its digits and the cube of its digits. &nbsp; &nbsp;&nbsp; 871 ??? &nbsp; &nbsp;&nbsp; 872 is a value of n for which n! + 1 is prime. &nbsp; &nbsp;&nbsp; 873 = 1! + 2! + 3! + 4! + 5! + 6! &nbsp; &nbsp;&nbsp; 874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2. &nbsp; &nbsp;&nbsp; 875 is 3-automorphic. &nbsp; &nbsp;&nbsp; 876 is a dodecagonal pyramidal number. &nbsp; &nbsp;&nbsp; 877 is the 7th Bell number. &nbsp; &nbsp;&nbsp; 878 is the number of 3×3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on a side. &nbsp; &nbsp;&nbsp; 879 is a number n whose 5th root has a decimal part that begins with the digits of n. &nbsp; &nbsp;&nbsp; 880 is the number of 4×4 magic squares. &nbsp; &nbsp;&nbsp; 881 is a number n whose 5th root has a decimal part that begins with the digits of n. &nbsp; &nbsp;&nbsp; 882 is the smallest number whose square begins with three 7's. &nbsp; &nbsp;&nbsp; 883 is a number n whose 5th root has a decimal part that begins with the digits of n. &nbsp; &nbsp;&nbsp; 884 is a number n whose 5th root has a decimal part that begins with the digits of n. &nbsp; &nbsp;&nbsp; 885 is an enneagonal pyramidal number. &nbsp; &nbsp;&nbsp; 886 ??? &nbsp; &nbsp;&nbsp; 887 is a value of n for which σ<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down&nbsp; &nbsp; (n)" loading="lazy" data-shortname="(n)" /> is a repdigit. &nbsp; &nbsp;&nbsp; 888 and the following 18 numbers are composite. &nbsp; &nbsp;&nbsp; 889 is a Kaprekar constant in base 2. &nbsp; &nbsp;&nbsp; 890 ??? &nbsp; &nbsp;&nbsp; 891 is the number of unlabeled distributive lattices with 15 elements. &nbsp; &nbsp;&nbsp; 892 is the smallest integer ratio of a 13-digit number to its product of digits. &nbsp; &nbsp;&nbsp; 893 ??? &nbsp; &nbsp;&nbsp; 894 has a base 5 representation that begins with its base 9 representation. &nbsp; &nbsp;&nbsp; 895 is a Woodall number. &nbsp; &nbsp;&nbsp; 896 is not the sum of 4 non-zero squares. &nbsp; &nbsp;&nbsp; 897 is a Cullen number. &nbsp; &nbsp;&nbsp; 898 is a member of the Fibonacci-type sequence starting with 2 and 5. &nbsp; &nbsp;&nbsp; 899 is the product of twin primes.</blockquote>

[QUOTE="MaD-DoC, post: 2312713, member: 56284"] 700 is the number of symmetric 8-cubes. 701 = 10 + 21 + 32 + 43 + 54. 702 ??? 703 is a Kaprekar number. 704 is the number of sided octominoes. 705 is the smallest Lucas pseudoprime. 706 ??? 707 is the smallest number whose reciprocal has period 12. 708 is the maximum value of n so that there exist 4 denominations of stamps so that every postage from 1 to n can be paid for with at most 12 stamps. 709 is the number of connected planar graphs with 9 edges. 710 is the number of connected graphs with 9 edges. 711 ??? 712 is the largest number known that does not have any digits in common with its 8th power. 713 is the number of commutative monoids of order 7 with 4 idempotents. 714 is the smallest number which has equal numbers of every digit in bases 2 and 5. 715 = 13C4. 716 is the smallest number whose cube contains four 6's. 717 is a palindrome in base 2 and in base 10. 718 is the number of unlabeled topologies with 6 elements. 719 is the number of rooted trees with 10 vertices. 720 = 6! 721 is the smallest number which can be written as the difference of 2 cubes in 2 ways. 722 is the sum of the 4th powers of the first 3 primes. 723 ??? 724 is the number of different arrangements of 10 non-attacking queens on an 10×10 chessboard. 725 ??? 726 is a pentagonal pyramidal number. 727 has the property that its square is the concatenation of two consecutive numbers. 728 is the smallest number n where n and n+1 are both products of 5 or more primes. 729 = 36. 730 is the number of connected bipartite graphs with 9 vertices. 731 is the number of planar partitions of 14. 732 = 17 + 26 + 35 + 44 + 53 + 62 + 71. 733 is the sum of the digits of 444. 734 is the smallest number that can be written as the sum of 3 distinct non-zero squares in 10 ways. 735 is the smallest number that is the concatenation of its distinct prime factors. 736 is a strong Friedman number. 737 ??? 738 = 6 + 66 + 666. 739 has a base 2 representation that begins with its base 9 representation. 740 is the number of self-avoiding walks of length 8. 741 is the number of multigraphs with 6 vertices and 8 edges. 742 is the smallest number that is one more than triple its reverse. 743 is the number of independent sets of the graph of the 4-dimensional hypercube. 744 is the number of perfect squared rectangles of order 14. 745 is the smallest number whose square begins with three 5's. 746 = 17 + 24 + 36. 747 ??? 748 is the number of 3×3 sliding puzzle positions that require exactly 12 moves to solve starting with the hole in a corner. 749 is the number of ways to divide a 7×7 grid of points into two sets using a straight line. 750 is the Stirling number of the second kind S(10,. 751 is the index of a prime Woodall number. 752 is the number of conjugacy classes in the automorphism group of the 11 dimensional hypercube. 753 is the smallest number whose cube contains 4 consecutive 7's. 754 ??? 755 is the number of trees on 14 vertices with diameter 6. 756 is the maximum number of regions space can be divided into by 14 spheres. 757 is the smallest number whose reciprocal has a period of 27. 758 ??? 759 ??? 760 is the number of partitions of 37 into distinct parts. 761 ??? 762 is the starting location of 999999 in the decimal expansion of π. 763 is the smallest number whose 4th power contains every digit at least once. 764 is the number of 8×8 symmetric permutation matrices. 765 is a Kaprekar constant in base 2. 766 is the number of series-reduced planted trees with 9 leaves. 767 is the largest n so that n2 = mC0 + mC1 + mC2 + mC3 has a solution. 768 is the number of subsets of {1,2,3,...,12} that have an integer average. 769 is the total number of digits of all binary numbers of length 1-7. 770 is the number of digits of the 15th perfect number. 771 is the number of intersections when all the diagonals of a regular 14-gon are drawn. 772 ??? 773 is the smallest odd number n so that n+2k is composite for all k<n. 774 ??? 775 is the smallest number whose 9th power has 26 digits. 776 ??? 777 is a repdigit in base 6 and in base 10. 778 is the number of ways a 5×1 rectangle can be surrounded by 5×1 rectangles. 779 ??? 780 = (5+7) × (5+× (5+0). 781 = 11111 in base 5. 782 is a number whose sum of divisors is a 4th power. 783 is the number of 11-ominoes that tile the plane by translation. 784 is the sum of the first 7 cubes. 785 are the last 3 digits of the sum of the first 785 squares. 786 is the largest known n for which 2nCn is not divisible by the square of an odd prime. 787 is a palindrome in base 3 and in base 10. 788 is the smallest of 6 consecutive numbers divisible by 6 consecutive primes. 789 are the first 3 digits of 9789. 790 ??? 791 is the smallest number n where either it or its neighbors are divisible by the numbers from 1 to 12. 792 is the number of partitions of 21. 793 is one less than twice its reverse. 794 = 16 + 26 + 36. 795 is a number whose sum of divisors is a 4th power. 796 ??? 797 is the number of functional graphs on 9 vertices. 798 is the number of ternary square-free words of length 16. 799 is the smallest number whose sum of digits is composite and whose sum of digits cubed is prime. 800 = 2222 in base 7. 801 = (7! + 8! + 9! + 10!) / (7 × 8 × 9 × 10). 802 is the number of isomers of C13H28. 803 is a value of n for which σ(n) is a repdigit. 804 is a value of n for which 2φ(n) = φ(n+1). 805 is the number of possible positions in Checkers after 4 moves. 806 is not the sum of a square, a cube, a 4th power, and a 5th power. 807 ??? 808 is a strobogrammatic number. 809 is a member of the Fibonacci-type sequence starting with 1 and 5. 810 is a value of n for which n-1 and n+1 are twin primes, and so are 2n-1 and 2n+1. 811 ??? 812 is the number of triangles of any size contained in the triangle of side 14 on a triangular grid. 813 are the first 3 digits of 813e. 814 is a value of n so that n(n+5) is a palindrome. 815 is a Lucas 3-step number. 816 = 18C3. 817 ??? 818 is the number of ways to dissect a 12-gon using non-crossing diagonals into polygons with an even number of sides. 819 is the smallest number so that it and its successor are both the product of 2 primes and the square of a prime. 820 = 1111 in base 9. 821 is a number n for which n, n+2, n+6, and n+8 are all prime. 822 is the number of planar graphs with 7 vertices. 823 is a number that does not have any digits in common with its cube. 824 ??? 825 is the number of ways to legally add 2 sets of parentheses to a product of 9 variables. 826 ??? 827 is the number of asymmetric trees with 11 vertices. 828 ??? 829 is a value of n for which π(n) is the product of the digits of n. 830 ??? 831 is the number of monic polynomials of degree 9 with integer coefficients whose complex roots are all in the unit disk. 832 is the maximum number of pieces a torus can be cut into with 16 cuts. 833 is a centered octahedral number. 834 is the maximum number of regions a cube can be cut into with 17 cuts. 835 is the 9th Motzkin number. 836 is a non-palindrome with a palindromic square. 837 ??? 838 ??? 839 has a base 5 representation that begins with its base 9 representation. 840 is the smallest number divisble by 1 through 8. 841 is a square that is also the sum of 2 consecutive squares. 842 is the ratio of Fibonacci numbers. 843 is the 14th Lucas number. 844 is the smallest number so that it and the next four numbers are squareful numbers. 845 ??? 846 has the property that its square is the concatenation of two consecutive numbers. 847 is the sum of the digits of the 14th Mersenne prime. 848 is the number of inequivalent binary linear codes of length 9. 849 is a value of n for which σ(n-1) = σ(n+1). 850 is the number of trees on 14 vertices with diameter 7. 851 is the number of ordered partitions of 18 into distinct parts. 852 is the number of 6-colorable connected graphs with 7 vertices. 853 is the number of connected graphs with 7 vertices. 854 has the property that it and its square together use the digits 1-9 once. 855 is the smallest number which is the sum of 5 consecutive squares or 2 consecutive cubes. 856 is a member of the Fibonacci-type sequence starting with 1 and 9. 857 is a value of n for which φ(n) = φ(n-1) + φ(n-2). 858 is the smallest palindrome with 4 different prime factors. 859 is the number of planar partitions of 11. 860 ??? 861 = 7 + 77 + 777. 862 is a number whose sum of divisors is a 4th power. 863 is a value of n so that n(n+6) is a palindrome. 864 is the number of partitions of 38 into distinct parts. 865 ??? 866 is the number of sided 10-iamonds. 867 is the number of graphs with 8 vertices that have chromatic number 5. 868 has a square root whose decimal part starts with the digits 1-9 in some order. 869 is the number of different resistances that can be created in a circuit of 9 equal resistors. 870 is the sum of its digits and the cube of its digits. 871 ??? 872 is a value of n for which n! + 1 is prime. 873 = 1! + 2! + 3! + 4! + 5! + 6! 874 is the number of positive integer solutions to (1 + 1/a)(1 + 1/b)(1 + 1/c)(1 + 1/d)(1 + 1/e) = 2. 875 is 3-automorphic. 876 is a dodecagonal pyramidal number. 877 is the 7th Bell number. 878 is the number of 3×3 sliding puzzle positions that require exactly 29 moves to solve starting with the hole on a side. 879 is a number n whose 5th root has a decimal part that begins with the digits of n. 880 is the number of 4×4 magic squares. 881 is a number n whose 5th root has a decimal part that begins with the digits of n. 882 is the smallest number whose square begins with three 7's. 883 is a number n whose 5th root has a decimal part that begins with the digits of n. 884 is a number n whose 5th root has a decimal part that begins with the digits of n. 885 is an enneagonal pyramidal number. 886 ??? 887 is a value of n for which σ(n) is a repdigit. 888 and the following 18 numbers are composite. 889 is a Kaprekar constant in base 2. 890 ??? 891 is the number of unlabeled distributive lattices with 15 elements. 892 is the smallest integer ratio of a 13-digit number to its product of digits. 893 ??? 894 has a base 5 representation that begins with its base 9 representation. 895 is a Woodall number. 896 is not the sum of 4 non-zero squares. 897 is a Cullen number. 898 is a member of the Fibonacci-type sequence starting with 2 and 5. 899 is the product of twin primes. [/QUOTE]

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