A353534 a(n) is the least prime p such that the numerator of the sum of reciprocals of the 2*n+1 consecutive primes starting with p is a prime.

2, 2, 5, 197, 7, 157, 29, 41, 2, 599, 3, 13, 293, 19, 181, 59, 7, 1489, 557, 43, 11, 23, 2, 227, 191, 349, 179, 2, 103, 5479, 2, 7, 131, 971, 37, 2, 6917, 23, 1279, 10903, 593, 311, 239, 2711, 6277, 1669, 257, 293, 503, 1861, 13613, 11, 569, 719, 619, 709, 4523, 3, 3, 2549, 1361, 383, 3, 10193

Offset: 1

Author

J. M. Bergot and Robert Israel, May 29 2022

Keywords

• nonn

Comments

We use 2*n+1 consecutive primes rather than n because the numerator of the sum of reciprocals of an even number of odd primes is even.

The numerators are in A354221.

Examples

			a(3) = 5 because the sum of reciprocals of 2*3 + 1 = 7 primes starting with 5 is 1/5 + 1/7 + 1/11 + 1/13 + 1/17 + 1/19 + 1/23 = 24749279/37182145, and 24749279 is prime.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..330

Crossrefs

Cf. A024451, A244622, A354221.

Programs

Maple

f:= proc(n) local i,k,v;
   for k from 1 do
     v:= numer(add(1/ithprime(i),i=k..k+2*n));
     if isprime(v) then return ithprime(k) fi
   od
end proc:
map(f, [$1..70]);