A345857 Numbers that are the sum of ten fourth powers in exactly five ways.

2935, 3110, 3190, 3205, 3270, 3445, 3814, 3940, 4165, 4180, 4195, 4215, 4245, 4260, 4290, 4310, 4325, 4375, 4420, 4435, 4615, 4660, 4675, 4695, 4774, 4805, 4854, 4869, 4870, 4900, 4934, 4965, 4999, 5029, 5030, 5044, 5045, 5095, 5110, 5125, 5140, 5174, 5235

Offset

1,1

Comments

Differs from A345598 at term 3 because 3175 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 = 1^4 + 1^4 + 2^4 + 2^4 + 2^4 + 5^4 + 5^4 + 5^4 + 5^4 + 5^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 6^4 + 6^4.

Links

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

Example

3110 is a term because 3110 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 + 6^4 + 6^4 = 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 4^4 + 4^4 + 7^4 = 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 + 6^4 + 6^4 = 2^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 4^4 + 7^4 = 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 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, 1000)]
for pos in cwr(power_terms, 10):
    tot = sum(pos)
    keep[tot] += 1
    rets = sorted([k for k, v in keep.items() if v == 5])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345598, A345807, A345847, A345856, A345858, A346350.

Sequence in context: A345579 A345836 A345598 * A365899 A236196 A054832

Adjacent sequences: A345854 A345855 A345856 * A345858 A345859 A345860

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved