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%I
%S 3,5,3,13,3,23,5,67,5,37,3,41,5,29,19,23,37,19,7,17,5,7,3,7,19,31,5,
%T 13,3,23,19,5,23,83,13,17,53,5,7,17,11,23,41,7,97,17,47,37,61,43,89,5,
%U 13,7,113,41,5,5,7,5,29,11,5,17,61,43,79,29,31,31,11,97,73,23,53,97,13,89,11,103
%N a(n) = prime(k) for the first k such that Product_{j=k..k+n-1} prime(j) mod Sum_{j=k..k+n-1} prime(j) is prime.
%H Robert Israel, <a href="/A336806/b336806.txt">Table of n, a(n) for n = 2..7700</a>
%e a(4) = 3 as 3*5*7*11 mod (3+5+7+11) = 11 is prime.
%p f:= proc(n) local L,k;
%p L:= [seq(ithprime(k),k=1..n)];
%p do
%p if isprime(convert(L,`*`) mod convert(L,`+`)) then return L[1] fi;
%p L:= [op(L[2..-1]),nextprime(L[-1])];
%p od;
%p end proc:
%p map(f, [$2..100]);
%K nonn
%O 2,1
%A _J. M. Bergot_ and _Robert Israel_, Jan 27 2021
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