A363759 Smallest number that can be written as a sum of a positive n-th power and a positive (n+1)-th power in 2 different ways.

5, 17, 4097, 1048577, 1073741825, 4398046511105, 72057594037927937, 4722366482869645213697, 1237940039285380274899124225, 1298074214633706907132624082305025, 5444517870735015415413993718908291383297

Offset

1,1

Links

Table of n, a(n) for n=1..11.

Example

5 = 1^1 + 2^2 = 4^1 + 1^2.
17 = 3^2 + 2^3 = 4^2 + 1^3.
4097 = 1^3 + 8^4 = 16^3 + 1^4.
1048577 = 1^4 + 16^6 = 32^5 + 1^6.

Prog

(PARI) a(n) = my(k=1); while (!(sum(j=1, k^(1/n), (k>j^n)*ispower(k-j^n, n+1))==2), k++); k;

Crossrefs

Cf. A000051, A016078.

Sequence in context: A253624 A085832 A062223 * A116911 A351890 A097491

Adjacent sequences: A363756 A363757 A363758 * A363760 A363761 A363762

Keyword

nonn

Author

Seiichi Manyama, Jun 20 2023

Status

approved