A003339 Numbers that are the sum of 5 positive 4th 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, 625, 629, 644, 659, 674, 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..10000 (first 1000 terms from T. D. Noe)

Eric Weisstein's World of Mathematics, Biquadratic Number.

Example

From David A. Corneth, Aug 04 2020: (Start)
22418 is in the sequence as 22418 = 1^4 + 2^4 + 7^4 + 10^4 + 10^4.
30004 is in the sequence as 30004 = 2^4 + 3^4 + 5^4 + 11^4 + 11^4.
39028 is in the sequence as 39028 = 5^4 + 5^4 + 7^4 + 11^4 + 12^4. (End)

Mathematica

Select[Range[1000], AnyTrue[PowersRepresentations[#, 5, 4], First[#]>0&]&] (* Jean-François Alcover, Jul 18 2017 *)

Prog

(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, 5))
  return sorted(s for s in ss if s <= limit)
print(aupto(800)) # Michael S. Branicky, May 20 2021

Crossrefs

Supersequence of A047716.

Cf. A000583, A003328, A003338, A003340, A003350, A344190, A344238.

Sequence in context: A063133 A029528 A101867 * A047716 A344190 A326005

Adjacent sequences: A003336 A003337 A003338 * A003340 A003341 A003342

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved