A274050 Numbers that cannot be expressed as the sum of two nonzero squares and at most one power of two.

1, 23, 71, 79, 95, 135, 142, 143, 167, 190, 191, 211, 215, 239, 255, 284, 286, 287, 303, 311, 323, 331, 343, 359, 380, 382, 383, 415, 419, 430, 431, 439, 455, 471, 475, 499, 503, 519, 527, 568, 572, 574, 575, 583, 591, 599, 622, 623, 646, 647, 671, 683, 695

Offset: 1

Author

Giovanni Resta, Jun 08 2016

Keywords

• nonn

Comments

The number 1 is considered a power of two.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Dave Platt, Tim Trudgian, On the sum of two squares and at most two powers of 2, arXiv:1610.01672 [math.NT], 2016.

Crossrefs

Cf. A000404, A273812.

Programs

Mathematica

nR[n_] := (SquaresR[2, n] + Plus @@ Pick[{-4, 4}, IntegerQ /@ Sqrt[{n, n/2}]])/8; bad[n_] := nR[n] == 0 && Block[{k = 1}, While[k < n && nR[n - k] == 0, k *= 2]; k >= n]; Select[Range@ 1000, bad]