A061068 Primes which are the sum of a prime and its subscript.

3, 5, 11, 19, 79, 101, 113, 127, 163, 173, 223, 271, 383, 419, 431, 503, 571, 599, 619, 641, 659, 673, 683, 701, 733, 757, 827, 863, 971, 1013, 1033, 1087, 1193, 1249, 1423, 1433, 1453, 1483, 1579, 1621, 1667, 1723, 2003, 2113, 2179, 2287, 2381, 2459, 2467

Offset: 1

Author

Labos Elemer, May 28 2001

Keywords

• nonn

Comments

a(n) = A061067(n-1) + A064402(n). - Leroy Quet, Jun 30 2006

This sequence is the intersection of A014688 with the set of primes. Conjecture: this sequence is infinite, yet derives from arbitrarily long "prime deserts" such as the 11 composites in A014688 between a(6) = 19 and a(18) = 79 and the 17 composites in A014688 between a(48) = 271 and a(66) = 383. - Jonathan Vos Post, Nov 22 2004

Primes not of the form n + pi(n-1). - Thomas Ordowski, Sep 21 2013

Except for the first pair (3, 5) no two consecutive primes are terms of the sequence. - Zak Seidov, Nov 10 2013

Examples

			5th term is 79=61+18=prime(18)+18.
		

Links

• T. D. Noe, Table of n, a(n) for n=1..1000

Crossrefs

Cf. A061067, A064402.

Programs

Mathematica

Select[Range[500], PrimeQ[Prime[ # ] + # ] &] + Prime[Select[Range[500], PrimeQ[Prime[ # ] + # ] &]] (* Stefan Steinerberger, Jul 21 2006 *)

PARI

{ n=0; m=0; forprime (p=2, 109567, if (isprime(p + m++), write("b061068.txt", n++, " ", p + m)) ) } \\ Harry J. Smith, Jul 17 2009

Extensions

Edited by N. J. A. Sloane, Apr 29 2007

Definition clarified by Jonathan Sondow, Jul 12 2012