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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.
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%I #9 Jun 01 2018 08:06:28

%S 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,

%T 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,

%U 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

%N 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.

%C The zeros are only conjectures (cf. A074981).

%C "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.

%e 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.

%e a(10) = 3 because 10 = 13^3 - 3^7.

%o (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

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

%K nonn

%O 1,1

%A _Zak Seidov_, Oct 13 2002

%E More terms from _David Wasserman_, Jan 23 2005

%E Edited and data double-checked with given PARI code by _M. F. Hasler_, May 29 2018