login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A047721
Sum of 10 but no fewer nonzero fourth powers.
2
10, 25, 40, 55, 70, 90, 105, 120, 135, 150, 160, 170, 185, 200, 215, 225, 230, 250, 265, 280, 295, 310, 330, 345, 360, 375, 390, 400, 410, 425, 440, 455, 465, 470, 485, 490, 505, 520, 535, 550, 565, 570, 585, 600, 615, 634, 640, 650, 665, 680, 695, 714, 730
OFFSET
1,1
LINKS
PROG
(PARI) upto(n)={my(e=10); 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 count, takewhile, combinations_with_replacement as mc
def aupto(lim):
p4 = list(takewhile(lambda x: x <= lim, (i**4 for i in count(1))))
s = [set(sum(c) for c in mc(p4, i) if sum(c) <= lim) for i in range(11)]
ans = s[10]
for i in range(1, 10):
ans -= s[i]
return sorted(ans)
print(aupto(730)) # Michael S. Branicky, Oct 25 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Arlin Anderson (starship1(AT)gmail.com)
STATUS
approved