A172425 -id:A172425 - cp's OEIS frontend

A133459 Sums of two nonzero pentagonal pyramidal numbers.

2, 7, 12, 19, 24, 36, 41, 46, 58, 76, 80, 81, 93, 115, 127, 132, 144, 150, 166, 197, 201, 202, 214, 236, 252, 271, 289, 294, 306, 322, 328, 363, 392, 406, 411, 414, 423, 445, 480, 484, 531, 551, 556, 568, 576, 590, 601, 625, 676, 693, 727, 732, 744, 746, 766

Offset: 1

Jonathan Vos Post, Dec 23 2007

nonn

Does this sequence ever include a pentagonal pyramidal number? That is, is it ever the case that A002411(i)=A002411(j)+A002411(k) as is often true for triangular pyramidal numbers (tetrahedral numbers) or square pyramidal numbers?

The answer to the above question is yes: A002411(30) + A002411(36) = 13950 + 23976 = 37926 = A002411(42) (see A172425). - Chai Wah Wu, Apr 16 2016

Cf. A002311, A002411, A053721, A172425.

nn = 12; Take[Union@ Map[Total, Tuples[#^2 (# + 1)/2 &@ Range@ nn, 2]], # (# - 1)/2 &[nn - 1]] (* Michael De Vlieger, Apr 16 2016 *)

{A002411(i) + A002411(j) for i, j > 0} = {i^2*(i+1)/2 + j^2*(j+1)/2 for i, j > 0}.

A172437 Indices of pentagonal pyramidal numbers which are the sum of two other such numbers: k such that A002411(k) = A002411(i)+A002411(j) for some i,j>0.

Original entry on oeis.org

42, 82, 171, 411, 522, 886, 1042, 1066, 1183, 1341, 2596, 2842, 3480, 3831, 5012, 5316, 5360, 5786, 6219, 6650, 6924, 8406, 8666, 9408, 10707, 11735, 12590, 12891, 14422, 14646, 14826, 17351, 17702, 17757, 18882, 23210, 24108, 25127, 28175, 31980, 32400

Offset: 1

M. F. Hasler, Nov 20 2010

nonn

The numbers themselves are listed in A172425. This answers a question posed in A133459.

			a(1)=42 because A002411(42) is the smallest term in that sequence which is the sum of two other (nonzero) terms of A002411.

Donovan Johnson, Table of n, a(n) for n = 1..160

Cf. A133459, A172425.

for(n=1,99999,for(m=1,n-1, isA002411(p(n)-p(m)) & !print1(n", ") & break)) /* needs isA002411() and p() */

cp's OEIS Frontend

A133459 Sums of two nonzero pentagonal pyramidal numbers.

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