A003342 Numbers that are the sum of 8 positive 4th powers.

8, 23, 38, 53, 68, 83, 88, 98, 103, 113, 118, 128, 133, 148, 163, 168, 178, 183, 193, 198, 213, 228, 243, 248, 258, 263, 278, 293, 308, 323, 328, 338, 343, 353, 358, 368, 373, 388, 403, 408, 418, 423, 433, 438, 453, 468, 483, 488, 498, 503, 518, 533, 548, 563, 568

Offset

1,1

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 04 2020: (Start)
5396 is in the sequence as 5396 = 1^4 + 1^4 + 4^4 + 5^4 + 5^4 + 6^4 + 6^4 + 6^4.
8789 is in the sequence as 8789 = 5^4 + 5^4 + 5^4 + 5^4 + 6^4 + 6^4 + 6^4 + 7^4.
12469 is in the sequence as 12469 = 1^4 + 3^4 + 4^4 + 4^4 + 5^4 + 5^4 + 5^4 + 10^4. (End)

Mathematica

Select[Range[500], AnyTrue[PowersRepresentations[#, 8, 4], First[#]>0&]&] (* Jean-François Alcover, Jul 18 2017 *)

Prog

(Python)
from itertools import combinations_with_replacement as mc
from sympy import integer_nthroot
def iroot4(n): return integer_nthroot(n, 4)[0]
def aupto(lim):
    pows4 = set(i**4 for i in range(1, iroot4(lim)+1) if i**4 <= lim)
    return sorted(t for t in set(sum(c) for c in mc(pows4, 8)) if t <= lim)
print(aupto(568)) # Michael S. Branicky, Aug 23 2021

Crossrefs

Cf. A000583, A003331, A003341, A003343, A003353, A345577, A345833.

Sequence in context: A341770 A287167 A253975 * A345833 A164284 A047719

Adjacent sequences: A003339 A003340 A003341 * A003343 A003344 A003345

Keyword

nonn,easy

Author

N. J. A. Sloane

Status

approved