%I #24 May 20 2021 08:38:38
%S 5,20,35,50,65,80,85,100,115,130,145,165,180,195,210,245,260,275,290,
%T 305,320,325,340,355,370,385,405,420,435,450,500,515,530,545,560,580,
%U 595,610,629,644,659,675,689,690,709,724,739,754,755,770,785,789,800
%N Sums of 5 but no fewer nonzero fourth powers.
%H David A. Corneth, <a href="/A047716/b047716.txt">Table of n, a(n) for n = 1..16998</a> (terms <= 200000)
%F Equals A003339 - A344189 - A344188 - A344187 - A000583. - _Sean A. Irvine_, May 15 2021
%o (PARI) upto(n)={my(e=5); my(s=sum(k=1, sqrtint(sqrtint(n)), x^(k^4)) + O(x*x^n)); my(p=s^e, q=(1 + s)^(e-1)); select(k->polcoeff(p,k) && !polcoeff(q,k), [1..n])} \\ _Andrew Howroyd_, Jul 06 2018
%o (Python)
%o from itertools import combinations_with_replacement as combs_with_rep
%o def aupto(limit):
%o qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 4 <= limit]
%o ss = [set(sum(c) for c in combs_with_rep(qd, k)) for k in range(6)]
%o return sorted(filter(lambda x: x <= limit, ss[5]-ss[4]-ss[3]-ss[2]-ss[1]))
%o print(aupto(800)) # _Michael S. Branicky_, May 20 2021
%Y Subsequence of A003339.
%Y Cf. A000583, A002377, A344187, A344188, A344189.
%K nonn
%O 1,1
%A Arlin Anderson (starship1(AT)gmail.com)
|