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%I #7 Sep 05 2012 13:29:44
%S 7,2,11,71,331,13,4217,4643,16381,6007,225217,260339,4772483,
%T 117351431,130554581,2499413753
%N Smallest prime q such that sum(i=1..n-1, q mod(prime(i))) == q mod prime(n).
%C The sequence is infinite.
%e n = 2: p_n = 3, q = 7,7 (mod 2) = 1 and 1 = 7 (mod 3);
%e n = 3: p_n = 5, q = 2, 2 (mod(2,3)) = (0,2) and 0 + 2 = 2 = 2 (mod 5);
%e n = 4: p_n = 7, q = 11, 11 (mod(2,3,5)) = (1,2,1) and 1 + 2 + 1 = 4 = 11 (mod 7);
%e n = 5: p_n = 11, q = 71, 71 (mod(2,3,5,7)) = (1,2,1,1) and 1 + 2 + 1 + 1 = 5 = 71 (mod 11).
%o (PARI) for(n=2,50,p=prime(n);q=2;while(sum(i=1,n-1,q%prime(i))<>q%p,q=nextprime(q+1));print(n","q))
%K nonn,more,hard
%O 2,1
%A _Zak Seidov_, Sep 02 2012
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