A351373 a(n) is the least prime that begins a sequence of 2*n consecutive primes whose sum is 6 times a prime.

5, 19, 89, 43, 103, 7, 19, 3, 19, 5, 67, 19, 31, 151, 19, 3, 3, 5, 61, 127, 61, 103, 13, 13, 137, 109, 149, 67, 59, 103, 59, 271, 983, 31, 3, 43, 277, 181, 3, 683, 307, 307, 83, 313, 181, 193, 331, 191, 151, 157, 151, 127, 151, 421, 523, 97, 97, 3, 5, 61, 61, 61, 331, 283, 283, 61, 167, 2003, 263

Offset: 1

Author

J. M. Bergot and Robert Israel, Feb 09 2022

Keywords

• nonn

Comments

Conjecture: each odd prime occurs infinitely many times.

Examples

			a(3) = 89 because the sum of the 6 consecutive primes starting with 89 is 89+97+101+103+107+109 = 606 = 6*101 where 101 is prime, and no smaller prime works.
		

Links

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

Crossrefs

Cf. A288632.

Programs

Maple

P:= select(isprime,[seq(i,i=3..10^5,2)]):
S:= [0,op(ListTools:-PartialSums(P))]:
nP:= nops(S):
f:= proc(n) local i, s;
  for i from 1 to nP-2*n do
    s:= S[i+2*n]-S[i];
    if s mod 6 = 0 and isprime(s/6) then return P[i] fi
  od
end proc:
map(f, [$1..100]);