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Message: <blockquote data-quote="MaD-DoC" data-source="post: 2312692" data-attributes="member: 56284">300 is the largest possible score in bowling. 301 is a 6-hyperperfect number. 302 is the number of ways to play the first 3 moves in Checkers. 303 is the number of bipartite graphs with 8 vertices. 304 is a primitive semiperfect number. 305 is an hexagonal prism number. 306 is the number of 5-digit triangular numbers. 307 is a non-palindrome with a palindromic square. 308 is a heptagonal pyramidal number. 309 is the smallest number whose 5th power contains every digit at least once. 310 = 1234 in base 6. 311 is a permutable prime. 312 = 2222 in base 5. 313 is the number of intersections when all the diagonals of a regular dodecagon are drawn. 314 is the smallest number that can be written as the sum of of 3 positive distinct squares in 6 ways. 315 = (4+3) × (4+1) × (4+5). 316 has a digit product which is the digit sum of (31)6. 317 is a value of n for which one less than the product of the first n primes is prime. 318 is the number of unlabeled partially ordered sets of 6 elements. 319 is the smallest number with the property that the partition with the largest product does not have a maximum number of parts. 320 is the maximum determinant of a binary 10×10 matrix. 321 is a Delannoy number. 322 is the 12th Lucas number. 323 is the product of twin primes. 324 is the largest possible product of positive integers with sum 16. 325 is a 3-hyperperfect number. 326 is the number of permutations of some subset of 5 elements. 327 is the largest number n so that n, 2n, and 3n together contain every digit from 1-9 exactly once. 328 concatenated with its successor is square. 329 is the number of forests with 10 vertices. 330 = 11C4. 331 is both a centered pentagonal number and a centered hexagonal number. 332 is the number of 2-connected graphs with 7 vertices 333 is the number of 7-hexes. 334 is the number of trees on 13 vertices with diameter 7. 335 is the number of degree 12 irreducible polynomials over GF(2). 336 = 8P3. 337 is the number of different resistances that can be created in a circuit of 8 equal resistors. 338 is the smallest number for which both the number of divisors and the sum of its prime factors is a perfect number. 339 is the number of ways to divide 5 black and 5 white beads into piles. 340 is a value of n for which n! + 1 is prime. 341 is the smallest pseudoprime in base 2. 342 is the number of inequivalent binary linear codes of length 8. 343 is a strong Friedman number. 344 is the smallest number that can be written as the sum of a cube and a 7th power in more than one way. 345 is half again as large as the sum of its proper divisors. 346 is a Franel number. 347 is a Friedman number. 348 is the smallest number whose 5th power contains exactly the same digits as another 5th power. 349 is a tetranacci number. 350 is the Stirling number of the second kind S(7,4). 351 is the smallest number so that it and the surrounding numbers are all products of 4 or more primes. 352 is the number of different arrangements of 9 non-attacking queens on an 9×9 chessboard. 353 is the smallest number whose 4th power can be written as the sum of four 4th powers. 354 is the sum of the first four 4th powers. 355 is the number of labeled topologies with 4 elements. 356 ??? 357 has a base 3 representation that ends with its base 7 representation. 358 has a base 3 representation that ends with its base 7 representation. 359 has a base 3 representation that ends with its base 7 representation. 360 is the number of degrees in a circle. 361 is the number of intersections on a go board. 362 and its double and triple all use the same number of digits in Roman numerals. 363 is a perfect totient number. 364 = 14C3. 365 is the smallest number that can be written as a sum of consecutive squares in more than 1 way. 366 is the number of days in a leap year. 367 is the largest number whose square has strictly increasing digits. 368 is the number of ways to tile a 4×15 rectangle with the pentominoes. 369 is the number of octominoes. 370 is a narcissistic number. 371 is a narcissistic number. 372 is a hexagonal pyramidal number. 373 is a permutable prime. 374 is the smallest number that can be written as the sum of 3 squares in 8 ways. 375 is a truncated tetrahedral number. 376 is an automorphic number. 377 is the 14th Fibonacci number. 378 is the maximum number of regions a cube can be cut into with 13 cuts. 379 is a value of n for which one more than the product of the first n primes is prime. 380 is the number of necklaces possible with 13 beads, each being one of 2 colors. 381 is a Kaprekar constant in base 2. 382 is the smallest number n with σ<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down    (n)" loading="lazy" data-shortname="(n)" /> = σ(n+3). 383 is the number of Hamiltonian graphs with 7 vertices. 384 = 8!! = 12!!!!. 385 is the number of partitions of 18. 386 is the number of regions the complex plane is cut into by drawing lines between all pairs of 11th roots of unity. 387 ??? 388 is the maximum value of n so that there exist 6 denominations of stamps so that every postage from 1 to n can be paid for with at most 6 stamps. 389 is the smallest prime so that it and the next 3 primes are all equal to 1 (mod 4). 390 is the number of partitions of 32 into distinct parts. 391 ??? 392 is a Kaprekar constant in base 5. 393 is the 7th central trinomial coefficient. 394 is a Schröder number. 395 does not occur in its factorial in base 2. 396 is the number of 3×3 sliding puzzle positions that require exactly 11 moves to solve starting with the hole in a corner. 397 is a Cuban prime. 398 is the number of integers with complexity 22. 399 is a Lucas-Carmichael number. 400 = 1111 in base 7.  401 is the number of connected planar Eulerian graphs with 9 vertices.  402 is the number of graphs with 8 vertices and 9 edges.  403 is the product of two primes which are reverses of each other.  404 is the number of sided 10-hexes with holes.  405 is a pentagonal pyramidal number.  406 is the number of ways to tile a 3×17 rectangle with 3×1 rectangles.  407 is a narcissistic number.  408 is the 8th Pell number.  409 is the number of graphs with 8 vertices with clique number 2.  410 is the smallest number that can be written as the sum of 2 distinct prime powers in 2 ways.  411 is a member of the Fibonacci-type sequence starting with 1 and 4.  412 is the number of subsets of {1,2,3,...,11} that have a sum divisible by 5.  413 is a structured hexagonal diamond number.  414 is a value of n for which n4, n5, n6, and n7 have the same digit sum.  415 ???  416 is the number of subsets of the 15th roots of unity that add to a real number.  417 is the smallest number so that it and the next 3 numbers have different numbers of distinct prime factors.  418 has the property that the sum of its prime factors is equal to the product of its digits.  419 is the number of ways to divide a 6×6 grid of points into two sets using a straight line.  420 is the smallest number divisible by 1 through 7.  421 is the number of commutative monoids of order 6.  422 is the smallest number whose 8th power has 21 digits.  423 is a number that does not have any digits in common with its cube.  424 ???  425 is the number of subsets of {1,2,3,...,11} that have an integer average.  426 is a stella octangula number.  427 is a value of n for which n! + 1 is prime.  428 has the property that its square is the concatenation of two consecutive numbers.  429 is the 7th Catalan number.  430 is the number of necklaces possible with 6 beads, each being one of 4 colors.  431 is the index of a prime Fibonacci number.  432 = 4 × 33 × 22.  433 is the index of a prime Fibonacci number.  434 is the smallest composite 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    (n)" loading="lazy" data-shortname="(n)" /> + 2 = σ(n+2).  435 is the number of ordered partitions of 16 into distinct parts.  436 is the smallest number whose cube contains four 8's.  437 has a cube with the last 3 digits the same as the 3 digits before that.  438 = 666 in base 8.  439 is the smallest prime where inserting the same digit between every pair of digits never yields another prime.  440 is the number of permutations of 12 items that fix 9 elements.  441 is the smallest square which is the sum of 6 consecutive cubes.  442 is the number of planar partitions of 13.  443 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    (n)" loading="lazy" data-shortname="(n)" /> is a repdigit.  444 is the largest known n for which there is a unique integer solution to a1+ ... +an = (a1)...(an).  445 has a base 10 representation which is the reverse of its base 9 representation.  446 is the smallest number that can be written as the sum of 3 distinct squares in 8 ways.  447 is the smallest number of convex quadrilaterals formed by 15 points in general position.  448 is the number of 10-iamonds.  449 has a base 3 representation that begins with its base 7 representation.  450 is the number of 13-iamonds with holes.  451 is the smallest number whose reciprocal has period 10.  452 is the closest integer to 7π.  453 is the only number n so that n, 2n, and 6n together contain every digit exactly once.  454 is the largest number known that cannot be written as a sum of 7 or fewer cubes.  455 = 15C3.  456 is the number of tournaments with 7 vertices.  457 is the index of a prime Euclid number.  458 is a number that does not have any digits in common with its cube.  459 is the smallest number n for which reverse<img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite23" alt="(n)" title="Thumbs down    (n)" loading="lazy" data-shortname="(n)" /> - n contains the same digits as n.  460 ???  461 is the number of ways to stack 18 pennies in contiguous rows so that each penny lies on the table or on two pennies.  462 = 11C5.  463 is the smallest prime so that it and the next 6 primes are all equal to 3 (mod 4).  464 is the maximum number of regions space can be divided into by 12 spheres.  465 is a Kaprekar constant in base 2.  466 = 1234 in base 7.  467 has strictly increasing digits in bases 7, 9, and 10.  468 = 3333 in base 5.  469 is a value of n for which n! - 1 is prime.  470 has a base 3 representation that ends with its base 6 representation.  471 is the smallest number with the property that its first 4 multiples contain the digit 4.  472 is the number of ways to tile a 5×5 square with integer-sided squares.  473 is the largest known number whose square and 4th power use different digits.  474 is a member of the Fibonacci-type sequence starting with 1 and 8.  475 has a square that is composed of overlapping squares of smaller numbers.  476 is the number of different products of subsets of the set {1, 2, 3, ... 11}.  477 is the smallest number whose cube contains four 3's.  478 is the 7th Pell-Lucas number.  479 is the number of sets of distinct positive integers with mean 6.  480 is the smallest number which can be written as the difference of 2 squares in 8 ways.  481 is the number of conjugacy classes in the automorphism group of the 10 dimensional hypercube.  482 is a number whose square and cube use different digits.  483 is the last 3-digit string in the decimal expansion of π.  484 is a palindrome in base 3 and in base 10.  485 is the number of categories with 6 morphisms and 2 objects.  486 is a Perrin number.  487 is the number of Hadamard matrices of order 28.  489 is an octahedral number.  490 is the number of partitions of 19.  491 is the smallest number n so that the largest prime factors of the numbers n through n+4 decrease.  492 is a hexanacci number.  493 is a Lucas 7-step number.  494 is the number of unlabeled distributive lattices with 14 elements.  495 is the Kaprekar constant for 3-digit numbers.  496 is the 3rd perfect number.  497 is the number of graphs with 8 edges.  498 is the number of necklaces possible with 8 beads, each being one of 3 colors.  499 is the number of ways to place 26 points on a 13×13 grid so that no 3 points are on a line.</blockquote>

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