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%I #26 Sep 08 2022 08:45:15
%S 5,7,13,19,29,67,97,113,229,293,307,401,409,439,613,643,659,709,739,
%T 809,829,859,937,1039,1051,1327,1483,1663,1693,1879,1999,2039,2113,
%U 2129,2239,2251,2549,2633,2707,2749,2753,2819,3041,3089,3137,3221,3271,3329
%N Primes p such that p + nextprime(p) is the arithmetic mean of a pair of twin primes.
%C This sequence (obviously) uses the "strictly larger" variant 2 (A151800) of the nextprime() function, rather than A007918. - _M. F. Hasler_, Sep 09 2015
%H Amiram Eldar, <a href="/A099349/b099349.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%t okQ[p_] := Module[{s = p + NextPrime[p]}, PrimeQ[s - 1] && PrimeQ[s + 1]]; Select[Prime[Range[1000]], okQ] (* _Zak Seidov_, Apr 10 2011 *)
%o (Magma) [n: n in PrimesUpTo(3330) | IsPrime(n+NextPrime(n)-1) and IsPrime(n+NextPrime(n)+1)]; // _Bruno Berselli_, Apr 10 2011
%o (PARI) is(n)=if(isprime(n),n+=nextprime(n+1); isprime(n-1) && isprime(n+1), 0) \\ _Charles R Greathouse IV_, Jul 01 2013
%Y Cf. A151800, A007918.
%K nonn,easy
%O 1,1
%A _Labos Elemer_, Nov 17 2004
%E Corrected and edited by _Zak Seidov_, Apr 10 2011
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