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A343196 a(n) is the least positive number k such that Sum_{k<=j<=k+n-1} A001414(j) is prime.

%I A343196 #11 Apr 09 2021 09:51:09
%S A343196 2,1,1,3,2,1,5,3,5,3,9,3,5,4,2,1,4,8,5,13,9,6,4,6,3,15,3,2,1,1,8,22,2,
%T A343196 1,1,1,3,2,1,9,5,9,5,3,6,3,3,5,8,5,6,31,11,9,4,2,1,2,1,3,5,4,9,9,5,5,
%U A343196 8,9,7,3,5,3,6,10,2,1,1,3,3,6,7,10,44,17,51,4,2,1,3,8,12,16,2,1,8
%N A343196 a(n) is the least positive number k such that Sum_{k<=j<=k+n-1} A001414(j) is prime.
%C A343196 a(n) is the first k such that the sum of primes, with repetition, dividing (k+n-1)!/(k-1)! is prime.
%H A343196 Robert Israel, <a href="/A343196/b343196.txt">Table of n, a(n) for n = 1..10000</a>
%e A343196 a(4) = 3 because A001414(3) + A001414(4) + A001414(5) + A001414(6) = 17 is prime.
%p A343196 sopf:= proc(n) option remember; local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
%p A343196 f:= proc(n) local j,t,i;
%p A343196   t:= add(sopf(i),i=1..n);
%p A343196   for j from 1  do
%p A343196     if isprime(t) then return j fi;
%p A343196     t:= t + sopf(j+n)-sopf(j)
%p A343196   od
%p A343196 end proc:
%p A343196 map(f, [$1..100]);
%Y A343196 Cf. A001414, A025281, A343197.
%K A343196 nonn
%O A343196 1,1
%A A343196 _J. M. Bergot_ and _Robert Israel_, Apr 07 2021