A047714 Sums of 3 but no fewer nonzero fourth powers.

3, 18, 33, 48, 83, 98, 113, 163, 178, 243, 258, 273, 288, 338, 353, 418, 513, 528, 593, 627, 642, 657, 707, 722, 768, 787, 882, 897, 962, 1137, 1251, 1266, 1298, 1313, 1328, 1331, 1378, 1393, 1458, 1506, 1553, 1568, 1633, 1808, 1875, 1922, 1937, 2002, 2177

Offset: 1

Author

Arlin Anderson (starship1(AT)gmail.com)

Keywords

• nonn

Comments

Identical to A003337 for n = 1..87. - Michael S. Branicky, Mar 18 2021

Links

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

Crossrefs

Cf. A000583, A002377, A336536, A344187.

Subsequence of A003337.

Programs

Maple

N:= 3000: # 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):
A:= sort(convert(F3 minus (F2 union F1), list)); # Robert Israel, Jul 24 2020

Python

def aupto(lim):
  p1 = set(i**4 for i in range(1, int(lim**.25)+2) if i**4 <= lim)
  p2 = set(a+b for a in p1 for b in p1 if a+b <= lim)
  p3 = set(apb+c for apb in p2 for c in p1 if apb+c <= lim)
  return sorted(p3-p2-p1)
print(aupto(2400)) # Michael S. Branicky, Mar 18 2021

Formula

A002377(a(n)) = 3. - Robert Israel, Jul 24 2020

Equals A003337 - A344187 - A000583. - Sean A. Irvine, May 15 2021