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Numbers that are sums (of a nonempty sequence) of consecutive centered square numbers.
6

%I #9 Dec 21 2018 16:50:47

%S 1,5,6,13,18,19,25,38,41,43,44,61,66,79,84,85,102,113,127,140,145,146,

%T 181,187,198,212,221,225,230,231,258,259,265,300,313,325,326,338,343,

%U 344,365,402,404,421,439,445,470,481,483,486,488,489,524,545,547,578,585,613,626,651,660

%N Numbers that are sums (of a nonempty sequence) of consecutive centered square numbers.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/CenteredSquareNumber.html">Centered Square Number</a>

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

%Y Cf. A001844, A005900, A034705, A320728, A322479, A322610, A322638, A322640.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Dec 20 2018