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

1,1

Comments

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

Links

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

Example

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.

Mathematica

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

Prog

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

Crossrefs

Cf. A151800, A007918.

Sequence in context: A045443 A153116 A227420 * A167464 A280266 A370008

Adjacent sequences: A099346 A099347 A099348 * A099350 A099351 A099352

Keyword

nonn,easy

Author

Labos Elemer, Nov 17 2004

Extensions

Corrected and edited by Zak Seidov, Apr 10 2011

Status

approved