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

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, 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, 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

Offset: 1

Author

J. M. Bergot and Robert Israel, Apr 07 2021

Keywords

• nonn

Comments

a(n) is the first k such that the sum of primes, with repetition, dividing (k+n-1)!/(k-1)! is prime.

Examples

			a(4) = 3 because A001414(3) + A001414(4) + A001414(5) + A001414(6) = 17 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001414, A025281, A343197.

Programs

Maple

sopf:= proc(n) option remember; local t; add(t[1]*t[2],t=ifactors(n)[2]) end proc:
f:= proc(n) local j,t,i;
  t:= add(sopf(i),i=1..n);
  for j from 1  do
    if isprime(t) then return j fi;
    t:= t + sopf(j+n)-sopf(j)
  od
end proc:
map(f, [$1..100]);