A230562 Smallest number that is the sum of 2 positive 4th powers in >= n ways.

0, 2, 635318657

Offset

0,2

Comments

Hardy and Wright say that a(3) is unknown.

Guy, 2004: "Euler knew that 635318657 = 133^4 + 134^4 = 59^4 + 158^4, and Leech showed this to be the smallest example. No one knows of three such equal sums."

References

R. K. Guy, Unsolved Problems in Number Theory, 3rd edition, Springer, 2004, D1

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 6th edition, 2008; section 21.11.

Links

Table of n, a(n) for n=0..2.

Carlos Rivera, Puzzle 103: N = a^4 + b^4 = c^4 + d^4

Example

0 = (empty sum).
2 = 1^4 + 1^4.
635318657 = 59^4 + 158^4 = 133^4 + 134^4.

Crossrefs

Cf. A003824, A016078, A018786, A046881, A088687, A088848, A088849, A088867, A230561.

Sequence in context: A322146 A262729 A034251 * A170999 A249482 A214600

Adjacent sequences: A230559 A230560 A230561 * A230563 A230564 A230565

Keyword

hard,more,nonn

Author

Jonathan Sondow, Oct 25 2013

Status

approved