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A099349
Primes p such that p + nextprime(p) is the arithmetic mean of a pair of twin primes.
21
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
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
Sequence in context: A045443 A153116 A227420 * A167464 A280266 A370008
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, Nov 17 2004
EXTENSIONS
Corrected and edited by Zak Seidov, Apr 10 2011
STATUS
approved