A271184 Löschian numbers (A003136) of the form k^2+1.

1, 37, 325, 577, 1297, 2917, 3601, 4357, 7057, 8101, 9217, 14401, 15877, 22501, 24337, 28225, 32401, 41617, 44101, 46657, 57601, 60517, 69697, 72901, 79525, 86437, 90001, 93637, 108901, 133957, 147457, 156817, 176401, 197137, 202501, 219025, 224677, 236197, 291601, 298117, 318097

Offset

1,2

Comments

Intersection of A002522 and A003136.

Corresponding values of k are 0, 6, 18, 24, 36, 54, 60, 66, 84, 90, 96, 120, 126, 150, 156, 168, 180, 204, 210, 216, 240, 246, 264, 270, 282, 294, 300, 306, ...

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Example

37 is a term because 37 = 6^2 + 1 = 4^2 + 4*3 + 3^2.

Mathematica

Select[Range[10^6], And[IntegerQ@Sqrt[# - 1], Resolve[Exists[{x, y}, Reduce[# == x^2 + x y + y^2, {x, y}, Integers]]]] &] (* Michael De Vlieger, Apr 01 2016 *)

Prog

(PARI) is(n) = #bnfisintnorm(bnfinit(z^2+z+1), n);
for(k=0, 2000, if(is(n=k^2+1), print1(n, ", ")));

Crossrefs

Cf. A002522, A003136.

Sequence in context: A114785 A061014 A130450 * A217117 A291859 A133554

Adjacent sequences: A271181 A271182 A271183 * A271185 A271186 A271187

Keyword

nonn

Author

Altug Alkan, Apr 01 2016

Status

approved