A003346 Numbers that are the sum of 12 positive 4th powers.

12, 27, 42, 57, 72, 87, 92, 102, 107, 117, 122, 132, 137, 147, 152, 162, 167, 172, 177, 182, 187, 192, 197, 202, 212, 217, 227, 232, 242, 247, 252, 257, 262, 267, 277, 282, 292, 297, 307, 312, 322, 327, 332, 342, 347, 357, 362, 372, 377, 387, 392, 402, 407, 412, 417

Offset

1,1

Comments

a(88) = 636 = 5^4 + 11 and a(91) = 651 = 5^4 + 2^4 + 10 are the first two terms not congruent to 2 or 7 (mod 10). - M. F. Hasler, Aug 03 2020

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 03 2020: (Start)
3740 is in the sequence as 3740 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 5^4 + 5^4 + 7^4.
4690 is in the sequence as 4690 = 2^4 + 2^4 + 2^4 + 2^4 + 2^4 + 4^4 + 4^4 + 4^4 + 5^4 + 5^4 + 6^4 + 6^4.
7193 is in the sequence as 7193 = 2^4 + 4^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 + 6^4. (End)

Prog

(PARI) (A003346_upto(N, k=12, m=4)=[i|i<-[1..#N=sum(n=1, sqrtnint(N, m), 'x^n^m, O('x^N))^k], polcoef(N, i)])(500) \\ 2nd & 3rd optional arg allow to get other sequences of this group. See A003333 for alternate code. - M. F. Hasler, Aug 03 2020
(Python)
from itertools import count, takewhile, combinations_with_replacement as mc
def aupto(limit):
    qd = takewhile(lambda x: x <= limit, (k**4 for k in count(1)))
    ss = set(sum(c) for c in mc(qd, 12))
    return sorted(s for s in ss if s <= limit)
print(aupto(417)) # Michael S. Branicky, Dec 27 2021

Crossrefs

Cf. A000583 (4th powers).

Other numbers that are the sum of k positive m-th powers:

A000404 (k=2, m=2), A000408 (3, 2), A000414 (4, 2), A047700 (k=5, m=2),

A003325 (k=2, m=3), A003072 (k=3, m=3), A003327 .. A003335 (k=4..12, m=3),

A003336 .. A003346 (k=2..12, m=4), A003347 .. A003357 (k=2..12, m=5),

A003358 .. A003368 (k=2..12, m=6), A003369 .. A003379 (k=2..12, m=7),

A003380 .. A003390 (k=2..12, m=8), A003391 .. A004801 (k=2..12, m=9),

A004802 .. A004812 (k=2..12, m=10), A004813 .. A004823 (k=2..12, m=11).

Sequence in context: A274897 A030736 A227854 * A047723 A151542 A069550

Adjacent sequences: A003343 A003344 A003345 * A003347 A003348 A003349

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved