A381855 Starting from prime(n), a(n) is the minimum number > 1 of consecutive primes whose sum is the lesser of a twin prime pair.

2, 95, 317, 23, 3, 5, 3, 3, 277, 7, 7, 25, 35, 237, 7, 5, 17, 41, 15, 33, 23, 7, 3, 111, 257, 3, 7, 57, 5, 11, 57, 13, 11, 79, 45, 67, 29, 97, 11, 15, 15, 21, 113, 19, 35, 15, 9, 5, 123, 29, 59, 27, 19, 227, 223, 37, 279, 53, 41, 3, 135, 53, 143, 81, 41, 29, 39, 63

Offset: 1

Author

Abhiram R Devesh, Mar 08 2025

Keywords

• nonn

Examples

			a(1) = 2 because we need to add the primes 2 and 3, to reach the lesser of the twin prime pair (5 and 7).
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001359.

Programs

PARI

a(n) = my(p=prime(n), q=nextprime(p+1), s = p+q, k=2); while (!(isprime(s) && isprime(s+2)), q=nextprime(q+1); s+=q; k++); k; \\ Michel Marcus, Mar 09 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)and sympy.isprime(s+2)):p=sympy.nextprime(p);s+=p;c+=1
   return c