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%I #24 Dec 02 2015 03:55:13
%S 5,37,53,67,157,173,211,257,263,277,373,479,563,593,607,613,631,653,
%T 733,809,947,977,1009,1103,1123,1187,1223,1297,1367,1471,1511,1607,
%U 1663,1721,1747,1753,1783,1867,1901,1907,1931,1993,2137,2287,2377,2411,2417
%N Primes that are the arithmetic mean of their prime predecessor and another prime.
%C prime(n) where 2*prime(n) - prime(n-1) is prime. - _Robert Israel_, Dec 01 2015
%H Robert Israel, <a href="/A071680/b071680.txt">Table of n, a(n) for n = 1..11000</a>
%e A000040(12) = 37, A000040(12-1) = 31, 37 = (31 + 43)/2, therefore 37 is a term.
%p Primes:= select(isprime, [2,seq(i,i=1..10^4,2)]):
%p Primes[select(i -> isprime(2*Primes[i]-Primes[i-1]), [$2..nops(Primes)])]; # _Robert Israel_, Dec 01 2015
%t p = q = 2; lst = {}; Do[q = Prime@n; If[PrimeQ[2q - p], AppendTo[lst, q]]; p = q, {n, 2, 400}]; lst (* _Robert G. Wilson v_, Mar 22 2007 *)
%o (PARI) lista(nn) = {forprime(p=5, nn, if (isprime(2*p-precprime(p-1)), print1(p, ", ")););} \\ _Michel Marcus_, Dec 01 2015
%Y Cf. A071681, A006562 is a subsequence.
%K nonn
%O 1,1
%A _Reinhard Zumkeller_, May 31 2002; revised Jul 16 2003
%E Thanks to _Sven Simon_ for noticing errors in the original version.
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