A274050 - OEIS

%I #13 Sep 04 2017 09:01:38

%S 1,23,71,79,95,135,142,143,167,190,191,211,215,239,255,284,286,287,

%T 303,311,323,331,343,359,380,382,383,415,419,430,431,439,455,471,475,

%U 499,503,519,527,568,572,574,575,583,591,599,622,623,646,647,671,683,695

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

%C The number 1 is considered a power of two.

%H Chai Wah Wu, <a href="/A274050/b274050.txt">Table of n, a(n) for n = 1..10000</a>

%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.

%t 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]

%Y Cf. A000404, A273812.

%K nonn

%O 1,2

%A _Giovanni Resta_, Jun 08 2016