A381868 Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the greater of a twin prime pair.

2, 137, 95, 3, 339, 93, 51, 5, 49, 5, 3, 115, 91, 35, 331, 7, 11, 3, 19, 29, 5, 187, 515, 15, 13, 79, 203, 11, 3, 69, 9, 93, 7, 13, 13, 5, 189, 71, 289, 419, 35, 239, 11, 9, 9, 33, 3, 129, 57, 75, 71, 53, 23, 121, 523, 13, 11, 3, 9, 11, 3, 193, 87, 5, 23, 181, 115, 3

Offset: 1

Author

Abhiram R Devesh, Mar 08 2025

Keywords

• nonn

Examples

			a(4) = 3 because we need to add the primes 7, 11 and 13, to reach the greater of the twin prime pair (29 and 31).
		

Links

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

Crossrefs

Cf. A006512, A381855, A381766.

Programs

Maple

f:= proc(p) local t,q,i;
  t:= p; q:= p;
  for i from 2 do
    q:= nextprime(q);
    t:= t+q;
    if isprime(t) and isprime(t-2) then return i fi
  od
end proc:
seq(f(ithprime(i)),i=1..100); # Robert Israel, May 08 2025

PARI

a(n) = my(p=prime(n), s=p, nb=1); while (!isprime(s-2) || !isprime(s) || (nb==1), p=nextprime(p+1); s+=p; nb++); nb; \\ Michel Marcus, Apr 02 2025

Python

import sympy
def a(n):
   p=sympy.prime(n); s=p; c=1
   p=sympy.nextprime(p); s+=p; c+=1
   while not(sympy.isprime(s-2) and sympy.isprime(s)):p=sympy.nextprime(p); s+=p; c+=1
   return c