|
%I #11 Apr 16 2016 20:47:17
%S 2,7,12,19,24,36,41,46,58,76,80,81,93,115,127,132,144,150,166,197,201,
%T 202,214,236,252,271,289,294,306,322,328,363,392,406,411,414,423,445,
%U 480,484,531,551,556,568,576,590,601,625,676,693,727,732,744,746,766
%N Sums of two nonzero pentagonal pyramidal numbers.
%C 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?
%C 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
%F {A002411(i) + A002411(j) for i, j > 0} = {i^2*(i+1)/2 + j^2*(j+1)/2 for i, j > 0}.
%t nn = 12; Take[Union@ Map[Total, Tuples[#^2 (# + 1)/2 &@ Range@ nn, 2]], # (# - 1)/2 &[nn - 1]] (* _Michael De Vlieger_, Apr 16 2016 *)
%Y Cf. A002311, A002411, A053721, A172425.
%K nonn
%O 1,1
%A _Jonathan Vos Post_, Dec 23 2007
|
