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

%I #7 Aug 30 2023 21:28:04

%S 1,2,5,7,9,10,11,13,15,16,17,22,25,26,28,31,34,36,37,40,41,43,46,49,

%T 50,51,52,55,56,58,61,64,65,66,67,70,71,73,76,78,79,81,82,85,91,93,96,

%U 97,101,103,106,107,109,111,115,116,120,121,126,127,130,131,133,135

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

%t nmax = 138; Position[CoefficientList[Series[Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^4, {j, 1, nmax^(1/4)}], {x, 0, nmax}], x] // Rest, 0] // Flatten

%Y Cf. A064233, A211167, A365166, A365167, A365168.

%K nonn

%O 1,2

%A _Ilya Gutkovskiy_, Aug 24 2023