A344188 Numbers that are the sum of three fourth powers in exactly one way

3, 18, 33, 48, 83, 98, 113, 163, 178, 243, 258, 273, 288, 338, 353, 418, 513, 528, 593, 627, 642, 657, 707, 722, 768, 787, 882, 897, 962, 1137, 1251, 1266, 1298, 1313, 1328, 1331, 1378, 1393, 1458, 1506, 1553, 1568, 1633, 1808, 1875, 1922, 1937, 2002, 2177, 2403, 2418, 2433, 2483, 2498, 2546, 2563, 2593, 2608, 2658

Offset

1,1

Comments

Differs from A003337 and A047714 at term 60 because 2673 = 2^4 + 4^4 + 7^4 = 3^4 + 6^4 + 6^4, see A309762.

Links

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

Example

33 is a member of this sequence because 33 = 1^4 + 2^4 + 2^4

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, 3):
    tot = sum(pos)
    keep[tot] += 1
rets = sorted([k for k, v in keep.items() if v == 1])
for x in range(len(rets)):
    print(rets[x])

Crossrefs

Cf. A003337, A025395, A344187, A344189, A344192, A344641.

Sequence in context: A161443 A003337 A047714 * A204192 A108169 A063116

Adjacent sequences: A344185 A344186 A344187 * A344189 A344190 A344191

Keyword

nonn

Author

David Consiglio, Jr., May 11 2021

Status

approved