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