A344193 Numbers that are the sum of four fourth powers in exactly two ways

259, 2674, 2689, 2754, 2929, 3298, 3969, 4144, 4209, 5074, 6579, 6594, 6659, 6769, 6834, 7203, 7874, 8194, 8979, 9154, 9234, 10113, 10674, 11298, 12673, 12913, 13139, 14674, 14689, 14754, 16563, 16643, 16818, 17187, 17234, 17299, 17314, 17858, 18963, 19699, 20658, 20739, 20979, 21154, 21219, 21329, 21363

Offset

1,1

Comments

Differs from A309763 at term 32 because 16578 = 1^4 + 2^4 + 9^4 + 10^4 = 2^4 + 5^4 + 6^4 + 11^4 = 3^4 + 7^4 + 8^4 + 10^4

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..20000

Example

2689 is a member of this sequence because 2689 = 2^4 + 2^4 + 4^4 + 7^4 = 2^4 + 3^4 + 6^4 + 6^4

Prog

(Python)
from itertools import combinations_with_replacement as cwr
from collections import defaultdict
keep = defaultdict(lambda: 0)
power_terms = [x**4 for x in range(1, 50)]
for pos in cwr(power_terms, 4):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 2])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A025404, A309763, A344189, A344192, A344237, A344242, A344645.

Sequence in context: A043376 A038480 A309763 * A254642 A322882 A256594

Adjacent sequences: A344190 A344191 A344192 * A344194 A344195 A344196

Keyword

nonn

Author

David Consiglio, Jr., May 11 2021

Status

approved