A360306 a(n) is the smallest positive integer which can be represented as the sum of n distinct nonzero fourth powers in exactly n ways, or -1 if no such integer exists.

1, 635318657, 811538, 300834, 185299, 138595, 143651, 154292, 197748, 225733, 291269, 374790, 474071, 586056, 715192, 857513, 1057689, 1330554, 1602250, 1919146, 2329547, 2786843, 3246204, 3899260, 4642700, 5378141, 6377822, 7342638, 8527103, 9787839, 11241455, 12978656

Offset

1,2

Links

Bert Dobbelaere, Table of n, a(n) for n = 1..79

Bert Dobbelaere, C++ program

Eric Weisstein's World of Mathematics, Biquadratic Number

Example

For n = 2: 635318657 = 59^4 + 158^4 = 133^4 + 134^4.
For n = 3: 811538 = 4^4 + 23^4 + 27^4 = 7^4 + 21^4 + 28^4 = 12^4 + 17^4 + 29^4.
For n = 4: 300834 = 1^4 + 4^4 + 12^4 + 23^4 = 1^4 + 16^4 + 18^4 + 19^4 = 3^4 + 6^4 + 18^4 + 21^4 = 7^4 + 14^4 + 16^4 + 21^4.

Crossrefs

Cf. A000583, A146756, A350241, A350270.

Sequence in context: A233848 A343077 A374579 * A018786 A003824 A348655

Adjacent sequences: A360303 A360304 A360305 * A360307 A360308 A360309

Keyword

nonn

Author

Ilya Gutkovskiy, Feb 02 2023

Extensions

a(18)-a(19) from Michael S. Branicky, Feb 04 2023

More terms from Bert Dobbelaere, Feb 11 2023

Status

approved