A063908 Numbers k such that k and 2*k-3 are primes.

3, 5, 7, 11, 13, 17, 23, 31, 37, 41, 43, 53, 67, 71, 83, 97, 101, 107, 113, 127, 137, 157, 167, 181, 191, 193, 211, 223, 233, 241, 251, 263, 283, 311, 317, 331, 347, 373, 421, 431, 433, 443, 457, 461, 487, 521, 547, 563, 577, 587, 613, 617, 631, 641, 643, 647

Offset

1,1

Comments

If p is in this sequence then the products of positive powers of 3, p and 2p-3 are entries in A086486. - Victoria A Sapko (vsapko(AT)canes.gsw.edu), Sep 23 2003

Median prime of AP3's starting at 3, i.e., triples of primes (3,p,q) in arithmetic progression. - M. F. Hasler, Sep 24 2009

a(n) = sum of the coprimes(p) mod (p+1). - J. M. Bergot, Nov 13 2014

A010051(2*a(n)-3) = 1. - Reinhard Zumkeller, Jul 02 2015

A098090 INTERSECT A000040. - R. J. Mathar, Mar 23 2017

Links

Harry J. Smith and K. D. Bajpai, Table of n, a(n) for n = 1..10000 (first 1000 terms from Harry J. Smith)

Carlos Rivera, Puzzle 34.- Prime Triplets in arithmetic progression, The Prime Puzzles & Problems Connection. [From M. F. Hasler, Sep 24 2009]

Formula

a(n) = A241817(n)/2. - Wesley Ivan Hurt, Apr 08 2018

Example

From K. D. Bajpai, Nov 29 2019: (Start)
a(5) = 13 is prime and 2*13 - 3 = 23 is also prime.
a(6) = 17 is prime and 2*17 - 3 = 31 is also prime.
(End)

Maple

select(k -> andmap(isprime, [k, 2*k-3]), [seq(k, k=1.. 10^4)]); # K. D. Bajpai, Nov 29 2019

Mathematica

Select[Prime[Range[6! ]], PrimeQ[2*#-3]&] (* Vladimir Joseph Stephan Orlovsky, Nov 17 2009 *)

Prog

(PARI) { n=0; p=1; for (m=1, 10^9, p=nextprime(p+1); if (isprime(2*p - 3), write("b063908.txt", n++, " ", p); if (n==1000, break)) ) } \\ Harry J. Smith, Sep 02 2009
(PARI) forprime( p=1, default(primelimit), isprime(2*p-3) && print1(p", ")) \\ M. F. Hasler, Sep 24 2009
(Magma) [n : n in [0..700] | IsPrime(n) and IsPrime(2*n-3)]; // Vincenzo Librandi, Nov 14 2014
(Haskell)
a063908 n = a063908_list !! (n-1)
a063908_list = filter
   ((== 1) . a010051' . (subtract 3) . (* 2)) a000040_list
-- Reinhard Zumkeller, Jul 02 2015

Crossrefs

Cf. A005382.

Cf. A000040, A010051, A088878, A172287.

Cf. A259730.

Sequence in context: A147545 A083668 A176116 * A154868 A274987 A020628

Adjacent sequences: A063905 A063906 A063907 * A063909 A063910 A063911

Keyword

nonn

Author

N. J. A. Sloane, Aug 31 2001

Status

approved