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

1,1

Comments

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

Links

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

Example

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

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 *)

Prog

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

Crossrefs

Cf. A071681, A006562 is a subsequence.

Sequence in context: A096673 A144960 A173826 * A141182 A127589 A244374

Adjacent sequences: A071677 A071678 A071679 * A071681 A071682 A071683

Keyword

nonn

Author

Reinhard Zumkeller, May 31 2002; revised Jul 16 2003

Extensions

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

Status

approved