A365169 Numbers that are not the sum of a prime number and a fourth power of a positive integer.

1, 2, 5, 7, 9, 10, 11, 13, 15, 16, 17, 22, 25, 26, 28, 31, 34, 36, 37, 40, 41, 43, 46, 49, 50, 51, 52, 55, 56, 58, 61, 64, 65, 66, 67, 70, 71, 73, 76, 78, 79, 81, 82, 85, 91, 93, 96, 97, 101, 103, 106, 107, 109, 111, 115, 116, 120, 121, 126, 127, 130, 131, 133, 135

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

N:= 30000: # for terms up to N
P:= select(isprime, {$2..N-1}):
F:= {seq(i^4, i=1..floor(N^(1/4)))}:
R:= {$1..N} minus select(`<=`, {seq(seq(s+t, s=P), t=F)}, N):
sort(convert(R, list)); # Robert Israel, May 08 2026

Mathematica

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

Crossrefs

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

Sequence in context: A349830 A241884 A291109 * A050114 A325171 A186155

Adjacent sequences: A365166 A365167 A365168 * A365170 A365171 A365172

Keyword

nonn

Author

Ilya Gutkovskiy, Aug 24 2023

Status

approved