A075789 - OEIS

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

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OFFSET

1,1

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.

LINKS

Table of n, a(n) for n=1..105.

EXAMPLE

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.

PROG

(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

CROSSREFS

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

Sequence in context: A239238 A125928 A114388 * A341018 A214323 A321865

Adjacent sequences: A075786 A075787 A075788 * A075790 A075791 A075792

KEYWORD

nonn

AUTHOR

Zak Seidov, Oct 13 2002

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

STATUS

approved