|
|
A047716
|
|
Sums of 5 but no fewer nonzero fourth powers.
|
|
2
|
|
|
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
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
LINKS
|
|
|
FORMULA
|
|
|
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]))
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
Arlin Anderson (starship1(AT)gmail.com)
|
|
STATUS
|
approved
|
|
|
|