A265109 a(n) = largest k such that prime(n) + A002110(k) is prime.

0, 1, 2, 3, 3, 4, 6, 7, 8, 6, 5, 9, 8, 8, 14, 9, 16, 17, 14, 14, 16, 21, 11, 19, 14, 24, 25, 15, 18, 11, 28, 12, 8, 19, 16, 22, 35, 31, 36, 25, 31, 16, 40, 30, 23, 41, 39, 35, 10, 32, 43, 38, 24, 41, 19, 35, 23, 55, 54, 24, 53, 50, 57, 62, 48, 36, 64, 21, 45, 54

Offset: 1

Author

Altug Alkan, Dec 01 2015

Keywords

• nonn

Comments

a(n) = n-1 iff a(n) is in A035346 for n > 1.

Examples

			a(4) = 3 because A002110(3) + prime(4) = A002110(3) + 7 = 37 is prime.
		

Links

• Michel Marcus, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A000040, A002110, A035346, A100380.

Programs

PARI

a(n) = {my(k=1); while(k, if(ispseudoprime(prod(i=1, n-k, prime(i)) + prime(n)), return(n-k)); k++)}

Python

from itertools import count
from sympy import isprime, prime, primorial
def A002110(n): return primorial(n) if n > 0 else 1
def A265109(n):
    pn = prime(n)
    return next(k for k in range(n-1, -1, -1) if isprime(pn+A002110(k)))
print([A265109(n) for n in range(1, 31)]) # Michael S. Branicky, Jan 10 2025

Formula

a(n) < n.