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 A063908 Numbers k such that k and 2*k-3 are primes. 29
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified September 26 08:20 EDT 2022. Contains 356993 sequences. (Running on oeis4.)