A047716 Sums of 5 but no fewer nonzero fourth powers.

5, 20, 35, 50, 65, 80, 85, 100, 115, 130, 145, 165, 180, 195, 210, 245, 260, 275, 290, 305, 320, 325, 340, 355, 370, 385, 405, 420, 435, 450, 500, 515, 530, 545, 560, 580, 595, 610, 629, 644, 659, 675, 689, 690, 709, 724, 739, 754, 755, 770, 785, 789, 800

Offset

1,1

Links

David A. Corneth, Table of n, a(n) for n = 1..16998 (terms <= 200000)

Formula

Equals A003339 - A344189 - A344188 - A344187 - A000583. - Sean A. Irvine, May 15 2021

Prog

(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
(Python)
from itertools import combinations_with_replacement as combs_with_rep
def aupto(limit):
  qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 4 <= limit]
  ss = [set(sum(c) for c in combs_with_rep(qd, k)) for k in range(6)]
  return sorted(filter(lambda x: x <= limit, ss[5]-ss[4]-ss[3]-ss[2]-ss[1]))
print(aupto(800)) # Michael S. Branicky, May 20 2021

Crossrefs

Subsequence of A003339.

Cf. A000583, A002377, A344187, A344188, A344189.

Sequence in context: A029528 A101867 A003339 * A344190 A326005 A063110

Adjacent sequences: A047713 A047714 A047715 * A047717 A047718 A047719

Keyword

nonn

Author

Arlin Anderson (starship1(AT)gmail.com)

Status

approved