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%I #4 Oct 01 2013 17:57:37
%S 2,7,9,11,16,19,20,22,23,25,28,29,30,31,32,33,35,36,37,39,40,41,45,46,
%T 49,52,54,56,62,64,66,68,69,70,79,80,81,82,83,85,88,91,96,98,102,103,
%U 108,110,114,116,117,118,119,122,123,126,131,136,143,144,148,150,154
%N Indices n such that the congruence prime(n)^x + prime(n+1)^x == prime(n+2) mod prime(n+3) has no solution.
%C Is this sequence infinite? Proof?
%e For index = 7 prime(7) = 17 and 17^x + 19^x ~= 23 mod 29 has no solutions.
%o (PARI) \No solutions to prime(i)^x+prime(i+1)^x ~= prime(i+2) mod prime(i+3) noanpbn(m,n) = { for(p=1,m, f=0; for(x=0,n, if((prime(p)^x+prime(p+1)^x-prime(p+2))%prime(p+3)==0,f=1) ); if( f==0,print1(p" ")) ) }
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, May 11 2003