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%I #11 Nov 25 2023 08:43:24
%S 2,6,16,17,18,20,21,25,29,31,33,35,36,41,45,52,53,59,61,62,64,65,77,
%T 79,81,83,84,85,88,90,91,94,95,96,100,101,102,103,104,106,110,114,116,
%U 117,119,122,132,136,137,139,147,152,154,155,156,157,158,164,167,172,173
%N Set of n such that the prime quadruple prime(n), prime(n+1), prime(n+2), prime(n+3) does not have a solution for the congruence prime(n+1)^x - prime(n)^x == prime(n+2) mod prime(n+3).
%e 2 is in the sequence because prime(2)=3, prime(2+1)=5, prime(2+2)=7, prime(2+3)=11 and 5^x-3^x == 7 mod 11 has no solutions.
%o (PARI) \\ Solutions to prime(i+1)^x-prime(i+1)^x == prime(i+2) mod prime(i+3).
%o noanmbn(m,n) = { for(p=1,m, f=0; for(x=0,n, if((prime(p+1)^x-prime(p)^x-prime(p+2))%prime(p+3)==0,f=1) ); if(f==0, print1(p ", ")) ) }
%Y Cf. A082371.
%K easy,nonn
%O 1,1
%A _Cino Hilliard_, May 11 2003