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 A005382 Primes p such that 2p-1 is also prime. (Formerly M0849) 115
 2, 3, 7, 19, 31, 37, 79, 97, 139, 157, 199, 211, 229, 271, 307, 331, 337, 367, 379, 439, 499, 547, 577, 601, 607, 619, 661, 691, 727, 811, 829, 877, 937, 967, 997, 1009, 1069, 1171, 1237, 1279, 1297, 1399, 1429, 1459, 1531, 1609, 1627, 1657, 1759, 1867, 2011 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Sequence gives values of p such Sum_{i=1..p} gcd(p,i) = A018804(p) is prime. - Benoit Cloitre, Jan 25 2002 Let q = 2n-1. For these n (and q), the sum of two cyclotomic polynomials can be written as a product of cyclotomic polynomials and as a cyclotomic polynomial in x^2: Phi(q,x) + Phi(2q,x) = 2 Phi(n,x) Phi(2n,x) = 2 Phi(n,x^2). - T. D. Noe, Nov 04 2003 Numbers n such that the n-th Hexagonal number A000384(n) = n*(2*n-1) is semiprime. {A005382} = {n such that A000384(n) is an element of A001358}. - Jonathan Vos Post, Feb 14 2006 Any prime of this form is a link in a Cunningham chain of the second kind, save the last term (ascending). - Raphie Frank, Sep 09 2012 Solutions of the equation (2*n-1)' + n' = 2, where n' is the arithmetic derivative of n. - Paolo P. Lava, Oct 31 2012 Primes in A006254. - Zak Seidov, Mar 26 2013 If a(n) is in A168421 then A005383(n) is a twin prime with a Ramanujan prime, A005383(n) - 2. If this sequence has an infinite number of terms in A168421, then the twin prime conjecture can be proved. - John W. Nicholson, Dec 05 2013 REFERENCES N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 870. R. P. Boas & N. J. A. Sloane, Correspondence, 1974 Ajeet Kumar, Subhamoy Maitra, and Chandra Sekhar Mukherjee, On approximate real mutually unbiased bases in square dimension, Cryptography and Communications (2020) Vol. 13, 321-329. Marius Tărnăuceanu, Arithmetic progressions in finite groups, arXiv:2003.10060 [math.GR], 2020. Wikipedia, Cunningham chain FORMULA a(n) = A129521(n) / A005383(n). - Reinhard Zumkeller, Apr 19 2007 a(n) = (A005383(n) + 1)/2. - Zak Seidov, Nov 04 2010 MAPLE f := proc(Q) local t1, i, j; t1 := []; for i from 1 to 500 do j := ithprime(i); if isprime(2*j-Q) then t1 := [op(t1), j]; fi; od: t1; end; f(1); MATHEMATICA Select[Prime[Range], PrimeQ[2#-1]&] PROG (MAGMA) [n: n in [0..1000] | IsPrime(n) and IsPrime(2*n-1)] // Vincenzo Librandi, Nov 18 2010 (PARI) select(p->isprime(2*p-1), primes(500)) \\ Charles R Greathouse IV, Apr 26 2012 (Haskell) a005382 n = a005382_list !! (n-1) a005382_list = filter    ((== 1) . a010051 . (subtract 1) . (* 2)) a000040_list -- Reinhard Zumkeller, Oct 03 2012 (PARI) forprime(n=2, 10^3, if(ispseudoprime(2*n-1), print1(n, ", "))) \\ Felix Fröhlich, Jun 15 2014 CROSSREFS Cf. A005383, A005384 (2p+1), A057326, A057327, A057328, A057329, A057330, A005603, A063908 (2p-3), A063909 (2p-5), A023204 (2p+3), A000384, A001358. Cf. A010051, A000040, A053685 (subsequence), A006254. Sequence in context: A334050 A073640 A174568 * A195354 A244638 A113165 Adjacent sequences:  A005379 A005380 A005381 * A005383 A005384 A005385 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified September 28 04:07 EDT 2021. Contains 347698 sequences. (Running on oeis4.)