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Numbers that cannot be expressed as the sum of two nonzero squares and at most two powers of two.
24

%I #23 Apr 23 2018 04:05:12

%S 1,535903,1072327,1594807,1750111,2025783,2822151,3304447,3566119,

%T 3697543,3855319,3982759,4874439,5832831,5930775,6642975,7115791,

%U 7536567,7591447,7885135,8058399,8225991,8307879,8357079,8900583,9339775,10071879,10626655,11274735,11334943,12046807,12229255

%N Numbers that cannot be expressed as the sum of two nonzero squares and at most two powers of two.

%C If up to three powers of 2 are allowed (instead of two), then the smallest n > 1 which cannot be expressed is larger than 10^10. - _Giovanni Resta_, Jun 08 2016

%C Smallest n > 1 that can't be written as the sum of two squares and at most three powers of two is larger than 2^36. - _David J. Platt_, Aug 11 2016

%H R. C. Crocker, <a href="https://www.impan.pl/en/publishing-house/journals-and-series/colloquium-mathematicum/all/112/2/87281/on-the-sum-of-two-squares-and-two-powers-of-k">On the sum of two squares and two powers of k</a>, Colloq. Math. 112(2008), 235-267.

%H Dave Platt, Tim Trudgian, <a href="https://arxiv.org/abs/1610.01672">On the sum of two squares and at most two powers of 2</a>, arXiv:1610.01672 [math.NT], 2016.

%Y Cf. A000404, A274050.

%K nonn

%O 1,2

%A _David J. Platt_, May 31 2016