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%I #27 Jul 17 2021 01:45:54
%S 0,7,0,7,7,15,0,31,7,15,7,7,15,23,0,7,31,7,7,23,15,17,7,31,7,7,15,15,
%T 23,7,0,7,7,39,31,15,7,17,7,7,23,15,15,7,17,7,7,31,31,23,7,23,7,7,15,
%U 17,15,7,23,7,7,17,0,17,7,15,7,7,39,15,31,7,15,7,7
%N a(n) is the smallest odd number k with GCD(k,n)=1 such that all the powers of 2 mod k are distinct from n mod k, or 0 if n is a power of 2.
%C All nonzero values are >= 7.
%e a(3) = 7 because the powers of 2 mod 7 are 2,4,1,2,4,1,2,4,1,2,4,... (and 3 never appears).
%o (PARI) a216185(n) = {local(k,m); if((omega(n) == 1) && (Mod(n,2) == Mod(0,2)), return(0), k=3; while(gcd(k,n) != 1 || (sum(m=0, eulerphi(k) - 1, (Mod(2,k)^m == Mod(n,k))) >= 1), k = k+2)); k} \\ _Michael B. Porter_, Mar 16 2013
%K nonn
%O 2,2
%A _J. Lowell_, Mar 11 2013
%E a(34)-a(76) from _Michael B. Porter_, Mar 16 2013