A365168 Numbers that are the sum of a prime number and a fourth power of a positive integer.

3, 4, 6, 8, 12, 14, 18, 19, 20, 21, 23, 24, 27, 29, 30, 32, 33, 35, 38, 39, 42, 44, 45, 47, 48, 53, 54, 57, 59, 60, 62, 63, 68, 69, 72, 74, 75, 77, 80, 83, 84, 86, 87, 88, 89, 90, 92, 94, 95, 98, 99, 100, 102, 104, 105, 108, 110, 112, 113, 114, 117, 118, 119, 122, 123, 124, 125

Offset: 1

Author

Ilya Gutkovskiy, Aug 24 2023

Keywords

• nonn

Links

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

Crossrefs

Cf. A058654, A307647, A365127, A365167, A365169.

Programs

Maple

N:= 200: # for terms up to N
P:= select(isprime,{$2..N-1}):
F:= {seq(i^4,i=1..floor(N^(1/4)))}:
sort(convert({seq(seq(s+t,s=P),t=F)},list)); # Robert Israel, Aug 28 2024

Mathematica

nmax = 125; f[x_] := Sum[x^Prime[i], {i, 1, nmax}] Sum[x^j^4, {j, 1, nmax^(1/4)}]; Exponent[#, x] & /@ List @@ Normal[Series[f[x], {x, 0, nmax}]]