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A274050 Numbers that cannot be expressed as the sum of two nonzero squares and at most one power of two. 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
The number 1 is considered a power of two.
LINKS
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
Sequence in context: A042040 A073035 A086104 * A274675 A188831 A183012
KEYWORD
nonn
AUTHOR
Giovanni Resta, Jun 08 2016
STATUS
approved

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Last modified June 15 19:43 EDT 2024. Contains 373410 sequences. (Running on oeis4.)