A047715 Numbers that are the sum of 4 but no fewer nonzero fourth powers.

4, 19, 34, 49, 64, 84, 99, 114, 129, 164, 179, 194, 244, 259, 274, 289, 304, 324, 339, 354, 369, 419, 434, 499, 514, 529, 544, 594, 609, 628, 643, 658, 673, 674, 708, 723, 738, 769, 784, 788, 803, 849, 868, 883, 898, 913, 963, 978, 1024, 1043, 1138, 1153

Offset

1,1

Comments

First differs from A003338 at term 64: A003338(64) = 1393 is also a term of A003337, so not a term here. - Michael S. Branicky, Apr 19 2021

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Formula

Equals A003338 - A344188 - A344187 - A000583, where "-" denotes "set difference". - Sean A. Irvine, May 15 2021

Maple

N:= 2000: # for terms <= N
F1:= {seq(i^4, i=1..floor(N^(1/4)))}: n1:= nops(F1):
F2:= select(`<=`, {seq(seq(F1[i]+F1[j], i=1..j), j=1..nops(F1))}, N):
F3:= select(`<=`, {seq(seq(s+t, s=F1), t=F2)}, N):
F4:= select(`<=`, {seq(seq(s+t, s=F1), t=F3)}, N):
sort(convert(((F4 minus F3) minus F2) minus F1, list)); # Robert Israel, Oct 11 2025

Prog

(Python)
limit = 1153
from functools import lru_cache
qd = [k**4 for k in range(1, int(limit**.25)+2) if k**4 + 3 <= limit]
qds = set(qd)
@lru_cache(maxsize=None)
def findsums(n, m):
  if m == 1: return {(n, )} if n in qds else set()
  return set(tuple(sorted(t+(q, ))) for q in qds for t in findsums(n-q, m-1))
A003338s = set(n for n in range(4, limit+1) if len(findsums(n, 4)) >= 1)
A003337s = set(n for n in range(3, limit+1) if len(findsums(n, 3)) >= 1)
A003336s = set(n for n in range(2, limit+1) if len(findsums(n, 2)) >= 1)
print(sorted(A003338s - A003337s - A003336s - qds)) # Michael S. Branicky, Apr 19 2021

Crossrefs

Cf. A000583, A002377, A003338 (sum of 4), A003337 (sum of 3), A003336 (sum of 2), A344188, A344187.

Sequence in context: A192193 A028564 A282506 * A003338 A344189 A031291

Adjacent sequences: A047712 A047713 A047714 * A047716 A047717 A047718

Keyword

nonn

Author

Arlin Anderson (starship1(AT)gmail.com)

Status

approved