A179295 a(n) is the least prime number such that prime(n)+a(n)+1 is a prime or -1 if no such prime number exists.

2, 3, 5, 3, 5, 3, 5, 3, 5, 7, 5, 3, 5, 3, 5, 5, 7, 5, 3, 7, 5, 3, 5, 7, 3, 5, 3, 5, 3, 13, 3, 5, 11, 11, 7, 5, 5, 3, 5, 5, 11, 11, 5, 3, 13, 11, 11, 3, 5, 3, 5, 11, 29, 5, 5, 5, 7, 5, 3, 11, 23, 13, 3, 5, 3, 13, 5, 11, 5, 3, 5, 7, 5, 5, 3, 5, 7, 3, 7, 11, 11

Offset: 1

Author

Lars-Erik Svahn, Jun 21 2017

Keywords

• nonn

Comments

If Maillet's conjecture is true, then a(n) != -1 for all n. - Chai Wah Wu, Aug 01 2017

Examples

			a(1) = 2, since prime(1) + 2 + 1 = 5.
		

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000
• Wen Huang and XiaoSheng Wu, On the set of the difference of primes, Proc. Amer. Math. Soc. 145 (2017), 3787-3793.
• E. Maillet, Réponse, L’intermédiaire des math. 12 (1905), p. 108.

Programs

Mathematica

Table[Block[{p=2}, While[!PrimeQ[Prime[n] + p + 1], p=NextPrime[p]]; p],{n, 100}] (* Indranil Ghosh, Jun 30 2017 *)

PARI

a(n) = my(pn=prime(n), p=2); while(! isprime(pn+p+1), p = nextprime(p+1)); p; \\ Michel Marcus, Jun 30 2017

Python

from sympy import prime, isprime, nextprime
def a(n):
    p=2
    while not isprime(prime(n) + p + 1): p=nextprime(p)
    return p
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 30 2017

Extensions

Definition clarified by Chai Wah Wu, Aug 01 2017

More terms from Chai Wah Wu, Aug 02 2017