A273812 Numbers that cannot be expressed as the sum of two nonzero squares and at most two powers of two.

1, 535903, 1072327, 1594807, 1750111, 2025783, 2822151, 3304447, 3566119, 3697543, 3855319, 3982759, 4874439, 5832831, 5930775, 6642975, 7115791, 7536567, 7591447, 7885135, 8058399, 8225991, 8307879, 8357079, 8900583, 9339775, 10071879, 10626655, 11274735, 11334943, 12046807, 12229255

Offset: 1

Author

David J. Platt, May 31 2016

Keywords

• nonn

Comments

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

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

Links

• R. C. Crocker, On the sum of two squares and two powers of k, Colloq. Math. 112(2008), 235-267.
• 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, A274050.