A344187 Numbers that are the sum of two positive fourth powers in exactly one way.

2, 17, 32, 82, 97, 162, 257, 272, 337, 512, 626, 641, 706, 881, 1250, 1297, 1312, 1377, 1552, 1921, 2402, 2417, 2482, 2592, 2657, 3026, 3697, 4097, 4112, 4177, 4352, 4721, 4802, 5392, 6497, 6562, 6577, 6642, 6817, 7186, 7857, 8192, 8962, 10001, 10016, 10081, 10256, 10625, 10657, 11296, 12401, 13122, 14096, 14642

Offset

1,1

Comments

Differs from A003336 at term 11660 because 635318657 = 59^4 + 158^4 = 133^4 + 134^4

Links

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

Example

32 is a member of this sequence because 32 = 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, 2):
    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. A003336, A338667, A344188.

Sequence in context: A078164 A060387 A003336 * A212740 A212742 A178145

Adjacent sequences: A344184 A344185 A344186 * A344188 A344189 A344190

Keyword

nonn

Author

David Consiglio, Jr., May 11 2021

Status

approved