A099349 Primes p such that p + nextprime(p) is the arithmetic mean of a pair of twin primes.

5, 7, 13, 19, 29, 67, 97, 113, 229, 293, 307, 401, 409, 439, 613, 643, 659, 709, 739, 809, 829, 859, 937, 1039, 1051, 1327, 1483, 1663, 1693, 1879, 1999, 2039, 2113, 2129, 2239, 2251, 2549, 2633, 2707, 2749, 2753, 2819, 3041, 3089, 3137, 3221, 3271, 3329

Offset: 1

Author

Labos Elemer, Nov 17 2004

Keywords

• nonn
• easy

Comments

This sequence (obviously) uses the "strictly larger" variant 2 (A151800) of the nextprime() function, rather than A007918. - M. F. Hasler, Sep 09 2015

Examples

			19 is a term since 19 + 23 = 42 is the sum of consecutive primes and also arithmetic mean of the twin primes 41 and 43.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A151800, A007918.

Programs

Magma

[n: n in PrimesUpTo(3330) | IsPrime(n+NextPrime(n)-1) and IsPrime(n+NextPrime(n)+1)];  // Bruno Berselli, Apr 10 2011

Mathematica

okQ[p_] := Module[{s = p + NextPrime[p]}, PrimeQ[s - 1] && PrimeQ[s + 1]]; Select[Prime[Range[1000]], okQ] (* Zak Seidov, Apr 10 2011 *)

PARI

is(n)=if(isprime(n),n+=nextprime(n+1); isprime(n-1) && isprime(n+1), 0) \\ Charles R Greathouse IV, Jul 01 2013

Extensions

Corrected and edited by Zak Seidov, Apr 10 2011