A341898 Numbers that are the sum of five fourth powers in exactly ten ways.

954979, 1205539, 1574850, 1713859, 1863859, 1877394, 1882579, 2071939, 2109730, 2225859, 2288179, 2419954, 2492434, 2495939, 2605314, 2711394, 2784499, 2835939, 2847394, 2880994, 2924674, 3007474, 3061939, 3071379, 3074179, 3117235, 3127219, 3174834, 3190899

Offset

1,1

Comments

Differs at term 5 because

1801459 = 1^4 + 4^4 + 5^4 + 28^4 + 33^4

= 1^4 + 4^4 + 12^4 + 23^4 + 35^4

= 1^4 + 7^4 + 16^4 + 30^4 + 31^4

= 1^4 + 16^4 + 18^4 + 19^4 + 35^4

= 3^4 + 6^4 + 18^4 + 21^4 + 35^4

= 5^4 + 7^4 + 19^4 + 24^4 + 34^4

= 5^4 + 9^4 + 14^4 + 29^4 + 32^4

= 7^4 + 9^4 + 16^4 + 25^4 + 34^4

= 7^4 + 14^4 + 16^4 + 21^4 + 35^4

= 8^4 + 9^4 + 20^4 + 29^4 + 31^4

= 10^4 + 19^4 + 19^4 + 21^4 + 34^4.

Links

David Consiglio, Jr., Table of n, a(n) for n = 1..10000

Example

954979 =  1^4 +  2^4 + 11^4 + 19^4 + 30^4
       =  1^4 +  7^4 + 18^4 + 25^4 + 26^4
       =  3^4 +  8^4 + 17^4 + 20^4 + 29^4
       =  4^4 +  8^4 + 13^4 + 25^4 + 27^4
       =  4^4 +  9^4 + 10^4 + 11^4 + 31^4
       =  6^4 +  6^4 + 15^4 + 21^4 + 29^4
       =  7^4 + 10^4 + 18^4 + 19^4 + 29^4
       = 11^4 + 11^4 + 20^4 + 22^4 + 27^4
       = 16^4 + 17^4 + 17^4 + 24^4 + 25^4
       = 18^4 + 19^4 + 20^4 + 23^4 + 23^4
so 954979 is a term.

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, 5):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 10])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A341892, A341897, A344929, A345188, A345822.

Sequence in context: A224593 A376473 A341897 * A092377 A348123 A022236

Adjacent sequences: A341895 A341896 A341897 * A341899 A341900 A341901

Keyword

nonn

Author

David Consiglio, Jr., Jun 04 2021

Status

approved