A345846 Numbers that are the sum of nine fourth powers in exactly four ways.

2854, 2919, 2934, 2949, 2964, 3014, 3029, 3094, 3159, 3174, 3204, 3254, 3269, 3429, 3444, 3558, 3573, 3638, 3798, 3813, 3974, 4034, 4134, 4164, 4179, 4182, 4209, 4214, 4274, 4294, 4389, 4439, 4454, 4534, 4614, 4644, 4709, 4773, 4788, 4838, 4884, 4918, 4949

Offset

1,1

Comments

Differs from A345588 at term 11 because 3189 = 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 1^4 + 3^4 + 4^4 + 4^4 + 6^4 + 6^4 = 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 = 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4.

Links

Sean A. Irvine, Table of n, a(n) for n = 1..10000

Example

2919 is a term because 2919 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 7^4.

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, 1000)]
for pos in cwr(power_terms, 9):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 4])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345588, A345796, A345836, A345845, A345847, A345856, A346339.

Sequence in context: A020429 A255026 A345588 * A233788 A250637 A067703

Adjacent sequences: A345843 A345844 A345845 * A345847 A345848 A345849

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved