login
Numbers that are sums of consecutive pentagonal numbers.
6

%I #49 Feb 16 2025 08:33:56

%S 0,1,5,6,12,17,18,22,34,35,39,40,51,57,69,70,74,75,86,92,108,117,120,

%T 121,125,126,145,156,162,176,178,190,195,196,209,210,213,247,248,262,

%U 270,279,282,287,288,321,330,354,365,376,386,387,399,404,405,424,425,438,457,475

%N Numbers that are sums of consecutive pentagonal numbers.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PentagonalNumber.html">Pentagonal Number</a>

%t anmax = 1000; nmax = Floor[Sqrt[2*anmax/3]] + 1; Select[Union[Flatten[Table[Sum[k*(3*k-1)/2, {k, i, j}], {i, 0, nmax}, {j, i, nmax}]]], # <= anmax &] (* _Vaclav Kotesovec_, Dec 21 2018 *)

%Y Cf. A000326, A002411, A034705, A034706, A319185, A322636, A322637.

%K nonn,changed

%O 1,3

%A _Ilya Gutkovskiy_, Dec 21 2018