A345854 Numbers that are the sum of ten fourth powers in exactly two ways.

265, 280, 295, 310, 325, 340, 345, 355, 360, 375, 390, 405, 420, 425, 440, 455, 470, 485, 505, 565, 580, 585, 595, 630, 645, 660, 665, 695, 710, 725, 745, 760, 805, 820, 835, 840, 870, 885, 889, 900, 904, 919, 920, 934, 935, 949, 950, 964, 965, 969, 984, 999

Offset

1,1

Comments

Differs from A345595 at term 20 because 520 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 4^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 3^4 + 3^4 + 3^4 + 4^4 = 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4 + 3^4.

Links

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

Example

280 is a term because 280 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 4^4 = 1^4 + 1^4 + 1^4 + 1^4 + 1^4 + 2^4 + 2^4 + 3^4 + 3^4 + 3^4.

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 == 2])
    for x in range(len(rets)):
        print(rets[x])

Crossrefs

Cf. A345595, A345804, A345844, A345853, A345855, A346347.

Sequence in context: A283665 A151602 A345595 * A051976 A255085 A146335

Adjacent sequences: A345851 A345852 A345853 * A345855 A345856 A345857

Keyword

nonn

Author

David Consiglio, Jr., Jun 26 2021

Status

approved