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

1,1

Comments

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

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

Formula

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A000040, A014692, A234694.

Sequence in context: A089438 A155777 A262839 * A067905 A042993 A308711

Adjacent sequences: A234692 A234693 A234694 * A234696 A234697 A234698

Keyword

nonn

Author

Zhi-Wei Sun, Dec 29 2013

Status

approved