

A071680


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


5



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
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OFFSET

1,1


COMMENTS

prime(n) where 2*prime(n)  prime(n1) is prime.  Robert Israel, Dec 01 2015


LINKS



EXAMPLE

A000040(12) = 37, A000040(121) = 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[i1]), [$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*pprecprime(p1)), print1(p, ", ")); ); } \\ Michel Marcus, Dec 01 2015


CROSSREFS



KEYWORD

nonn


AUTHOR



EXTENSIONS

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


STATUS

approved



