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Numbers that are not the sum of a prime number and a fourth power of a nonnegative integer.
3

%I #7 Aug 30 2023 21:27:26

%S 1,9,10,15,16,22,25,26,28,34,36,40,46,49,50,51,52,55,56,58,64,65,66,

%T 70,76,78,81,82,85,91,93,96,106,111,115,116,120,121,126,130,133,135,

%U 136,141,144,145,146,156,159,161,162,166,169,171,172,175,176,177,185,186,187,196

%N Numbers that are not the sum of a prime number and a fourth power of a nonnegative integer.

%t nmax = 197; Position[CoefficientList[Series[Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^4, {j, 0, nmax^(1/4)}], {x, 0, nmax}], x] // Rest, 0] // Flatten

%Y Cf. A014090, A045911, A356295, A365126, A365127, A365169.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 24 2023