A377306 Numbers that are not the sum of the first k fourth powers.

2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69

Offset

1,1

Comments

Complement of A000538.

Links

Table of n, a(n) for n=1..67.

Formula

a(n) = n+m if 30n > m(m-1)(6m^3+21m^2+31m+31) and a(n) = n+m-1 otherwise, where m = floor((5n)^(1/5)).

Mathematica

lim=69; l4=Ceiling[lim^(1/4)]; Complement[Range[lim], Accumulate[Range[0, l4]^4]] (* James C. McMahon, Oct 24 2024 *)

Prog

(Python)
from sympy import integer_nthroot
def A377306(n): return n+(m:=integer_nthroot(5*n, 5)[0])-(30*n<=m*(m-1)*(m*(m*(3*((m<<1)+7))+31)+31))

Crossrefs

Cf. A133137, A000330, A000537, A302058, A376573, A000538, A376745.

Sequence in context: A023771 A132033 A194966 * A133137 A160543 A023810

Adjacent sequences: A377303 A377304 A377305 * A377307 A377308 A377309

Keyword

nonn,easy

Author

Chai Wah Wu, Oct 23 2024

Status

approved