A234695 Primes p with prime(p) - p + 1 also prime.

2, 3, 5, 7, 13, 17, 23, 31, 41, 43, 61, 71, 83, 89, 103, 109, 139, 151, 173, 181, 199, 211, 223, 241, 271, 277, 281, 293, 307, 311, 317, 337, 349, 353, 367, 463, 499, 541, 563, 571, 601, 661, 673, 709, 719, 743, 751, 757, 811, 823, 827, 883, 907, 911, 953

Offset: 1

Author

Zhi-Wei Sun, Dec 29 2013

Keywords

• nonn

Comments

By the conjecture in A234694, this sequence should have infinitely many terms.

Examples

			a(1) = 2 since prime(2) - 1 = 2 is prime.
a(2) = 3 since prime(3) - 2 = 3 is prime.
a(3) = 5 since prime(5) - 4 = 7 is prime.
a(4) = 7 since prime(7) - 6 = 11 is prime.
		

Links

• Zhi-Wei Sun, Table of n, a(n) for n = 1..10000
• Z.-W. Sun, Problems on combinatorial properties of primes, arXiv:1402.6641, 2014

Crossrefs

Cf. A000040, A014692, A234694.

Programs

Mathematica

n=0;Do[If[PrimeQ[Prime[Prime[k]]-Prime[k]+1],n=n+1;Print[n," ",Prime[k]]],{k,1,1000}]

PARI

forprime(p=1,999,isprime(prime(p)-p+1)&&print1(p",")) \\ - M. F. Hasler, Dec 31 2013

Formula

a(n) = prime(A234852(n)). - M. F. Hasler, Dec 31 2013