A239527 Numbers k^2 + (k+1)^2 that can be expressed as a sum of two squares in exactly one other way.

85, 145, 221, 265, 365, 481, 545, 685, 1405, 1513, 1985, 2245, 2813, 2965, 3281, 3785, 3961, 4141, 4705, 5305, 5513, 5941, 6161, 6385, 6613, 7081, 7813, 8065, 8321, 9113, 9385, 10805, 11101, 11401, 11705, 12013, 12961, 13285, 13945, 16021, 17113, 17861, 19405

Offset

1,1

Comments

Subsequence of A166080.

Links

Giovanni Resta, Table of n, a(n) for n = 1..10000

Formula

Each number is of the form 2y^2 + 2y + 1.

Example

365 is in the sequence because 365 = 2^2+19^2 = 13^2+14^2; in the second representation 14-13=1.

Mathematica

ok[n_] := 2 == Count[ PowersRepresentations[n, 2, 2], _?(! MemberQ[#, 0] &)]; Select[(2*#^2 + 2*# + 1) & /@ Range[100], ok] (* Giovanni Resta, Mar 21 2014 *)

Crossrefs

Cf. A166080, A000404, A001844.

Sequence in context: A027453 A259219 A273123 * A029471 A083750 A043684

Adjacent sequences: A239524 A239525 A239526 * A239528 A239529 A239530

Keyword

nonn

Author

Carmine Suriano, Mar 21 2014

Status

approved