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

1,2

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.

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]

Crossrefs

Cf. A000404, A273812.

Sequence in context: A042040 A073035 A086104 * A274675 A188831 A183012

Adjacent sequences: A274047 A274048 A274049 * A274051 A274052 A274053

Keyword

nonn

Author

Giovanni Resta, Jun 08 2016

Status

approved