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This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A113941 Pentagonal numbers (A000326) that are also brilliant numbers (A078972).

Original entry on oeis.org

35, 247, 1247, 2501, 4187, 15251, 17767, 33227, 49051, 63551, 68587, 71177, 76501, 81317, 96647, 112477, 118301, 128627, 147737, 159251, 182527, 241001, 250717, 265651, 302177, 318551, 438751, 485357, 563347, 655051, 1563151, 1600117
Offset: 1

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Author

Giovanni Resta, Jan 31 2006

Keywords

Comments

This is to pentagonal numbers A000326 as A113940 is to triangular numbers A000217. These may be seen as the 5th and 3rd row of an infinite array of k-gonal numbers which are also brilliant numbers, where the 4th row is A001248 squares of primes. - Jonathan Vos Post, Apr 05 2009

Examples

			a(1) = 35 = 5th pentagonal number = 5*(3*5-1)/2 = 5 * 7, with the two prime factors each being one digit in length. a(2) = 247 = 13th pentagonal number = 13*(3*13-1)/2 = 13 * 19, with the two prime factors each being two digits in length. a(6) = 15251 = 101 * 151, with the two prime factors each being three digits in length. - _Jonathan Vos Post_, Apr 05 2009
17767 is the 109th pentagonal number and 17767=109*163 is brilliant.

Crossrefs

Cf. A000326, A078972, A159190.
Cf. A001222, A001248, A001358, A113940, A114439.

Formula

A000326 INTERSECTION A078972.

Extensions

Edited by N. J. A. Sloane, Apr 07 2009 at the suggestion of R. J. Mathar
Two more terms from R. J. Mathar, Apr 06 2009
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Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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