cp's OEIS Frontend

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.

%I A075789 #9 Jun 01 2018 08:06:28
%S A075789 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 A075789 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 A075789 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 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.
%C A075789 The zeros are only conjectures (cf. A074981).
%C A075789 "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 A075789 1 = 3^2 - 2^3, 2 = 3^3 - 5^2, 3 = 2^2 - 1^2, 4 = 2^3 - 2^2, etc.
%e A075789 a(10) = 3 because 10 = 13^3 - 3^7.
%o A075789 (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 A075789 Cf. A074981 (not difference of powers), A075788, A075790, A075791.
%K A075789 nonn
%O A075789 1,1
%A A075789 _Zak Seidov_, Oct 13 2002
%E A075789 More terms from _David Wasserman_, Jan 23 2005
%E A075789 Edited and data double-checked with given PARI code by _M. F. Hasler_, May 29 2018