A071680 Primes that are the arithmetic mean of their prime predecessor and another prime.

5, 37, 53, 67, 157, 173, 211, 257, 263, 277, 373, 479, 563, 593, 607, 613, 631, 653, 733, 809, 947, 977, 1009, 1103, 1123, 1187, 1223, 1297, 1367, 1471, 1511, 1607, 1663, 1721, 1747, 1753, 1783, 1867, 1901, 1907, 1931, 1993, 2137, 2287, 2377, 2411, 2417

Offset: 1

Author

Reinhard Zumkeller, May 31 2002; revised Jul 16 2003

Keywords

• nonn

Comments

prime(n) where 2*prime(n) - prime(n-1) is prime. - Robert Israel, Dec 01 2015

Examples

			A000040(12) = 37, A000040(12-1) = 31, 37 = (31 + 43)/2, therefore 37 is a term.
		

Links

• Robert Israel, Table of n, a(n) for n = 1..11000

Crossrefs

Cf. A071681, A006562 is a subsequence.

Programs

Maple

Primes:= select(isprime, [2,seq(i,i=1..10^4,2)]):
Primes[select(i -> isprime(2*Primes[i]-Primes[i-1]), [$2..nops(Primes)])]; # Robert Israel, Dec 01 2015

Mathematica

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 *)

PARI

lista(nn) = {forprime(p=5, nn, if (isprime(2*p-precprime(p-1)), print1(p, ", ")););} \\ Michel Marcus, Dec 01 2015

Extensions

Thanks to Sven Simon for noticing errors in the original version.