A064402 Numbers n such that prime(n)+n is a prime, where prime(n) denotes the n-th prime number.

1, 2, 4, 6, 18, 22, 24, 26, 32, 34, 42, 48, 66, 70, 72, 82, 92, 96, 98, 100, 102, 104, 106, 108, 114, 116, 126, 130, 144, 150, 152, 158, 172, 180, 200, 202, 204, 206, 218, 222, 228, 236, 270, 282, 290, 300, 312, 322, 324, 328, 330, 350, 352, 356, 362, 378, 384

Offset: 1

Author

Robert G. Wilson v, Sep 28 2001

Keywords

• nonn

Comments

a(n) = order among the primes of A061067(n).

Except for the first one all terms are even. Conjecture: First differences include all even integers. - Zak Seidov, Nov 10 2013

Links

• Harry J. Smith, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A061067, A061068, A064269.

Programs

Magma

[n: n in [0..500]| IsPrime(NthPrime(n) +n)]; // Vincenzo Librandi, Apr 06 2011

Mathematica

Select[ Range[ 400 ], PrimeQ[ Prime[ # ] + # ] & ]

PARI

{ n=0; for (m=1, 10^9, if (isprime(prime(m) + m), write("b064402.txt", n++, " ", m); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 13 2009

Formula

a(n) = A061068(n) - A061067(n-1).

A014688(a(n)) = A061068(n). - Zak Seidov, Nov 10 2013

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 08 2007