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A071680 Primes that are the arithmetic mean of their prime predecessor and another prime. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 20 22:44 EDT 2019. Contains 328291 sequences. (Running on oeis4.)