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

Author

Jonathan Vos Post, Dec 23 2007

Keywords

• nonn

Comments

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

Crossrefs

Cf. A002311, A002411, A053721, A172425.

Programs

Mathematica

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

Formula

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