A381766 Starting from the n-th prime, a(n) is the minimum number > 1 of consecutive primes whose sum is the average of a twin prime pair.

57, 180, 2, 2, 4, 2, 8, 2, 100, 2, 16, 18, 26, 12, 160, 4, 70, 70, 2, 12, 6, 4, 76, 202, 2, 4, 4, 10, 24, 2, 14, 18, 22, 8, 8, 48, 4, 72, 132, 224, 180, 142, 10, 96, 24, 10, 24, 124, 76, 2, 164, 34, 196, 120, 34, 24, 128, 118, 8, 6, 34, 2, 2, 8, 116, 18, 552, 6

Offset: 1

Author

Abhiram R Devesh, Mar 08 2025

Keywords

• nonn

Examples

			a(3) = 2 because we need to add 5 and 7, to reach the average of the twin primes 11 and 13, which is 12.
		

Crossrefs

Cf. A065091, A014574, A381868.

Programs

Maple

A381766 := proc(n)
    local p ,a, ps;
    p := ithprime(n) ;
    ps := p ;
    for a from 2 do
        p := nextprime(p) ;
        ps := ps+p ;
        if isprime(ps-1) and isprime(ps+1) then
            return a;
        end if;
    end do:
end proc:
seq(A381766(n),n=1..20) ; # R. J. Mathar, Apr 02 2025

PARI

a(n) = my(p=prime(n), s=p, nb=1); while (!isprime(s-1) || !isprime(s+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
   while not(sympy.isprime(s-1) and sympy.isprime(s+1)):p=sympy.nextprime(p);s+=p;c+=1
   return c