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URL: https://oeis.org/A063908

⇱ A063908 - OEIS

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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
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Aug 31 2001
STATUS
approved