A075789 Value of i, when n is written as r^i - s^j with the smallest possible r^i (with minimal i) and r, s > 0, i, j > 1; or 0 if n is not of this form.

2, 3, 2, 3, 2, 0, 3, 2, 2, 3, 3, 2, 2, 0, 2, 2, 2, 3, 3, 2, 2, 2, 3, 2, 3, 3, 2, 5, 2, 2, 5, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 3, 2, 2, 7, 2, 2, 0, 2, 2, 2, 2, 2, 2, 2, 0, 2, 2, 3, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 5, 2, 3, 2, 0, 7, 2, 2, 0, 2, 2, 2, 0, 2, 2, 2, 0, 2, 2, 3, 2, 2, 2, 2, 3, 2, 3, 7, 0, 7, 2, 2

Offset: 1

Author

Zak Seidov, Oct 13 2002

Keywords

• nonn

Comments

The zeros are only conjectures (cf. A074981).

"minimal i" means that, if r^i = a^b with composite b, then i is the smallest prime factor of b; e.g., r^i = 3^4 = 9^2, i.e., r = 9, i = 2.

Examples

			1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
a(10) = 3 because 10 = 13^3 - 3^7.
		

Crossrefs

Cf. A074981 (not difference of powers), A075788, A075790, A075791.

Programs

PARI

a(n,LIM=999*n)=for(k=1,LIM,(ispower(k)||k==1)&&ispower(n+k)&&return(factor(ispower(n+k))[1,1])) \\ M. F. Hasler, May 29 2018

Extensions

More terms from David Wasserman, Jan 23 2005

Edited and data double-checked with given PARI code by M. F. Hasler, May 29 2018