# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/ Search: id:a005382 Showing 1-1 of 1 %I A005382 M0849 #102 Feb 05 2024 00:56:58 %S A005382 2,3,7,19,31,37,79,97,139,157,199,211,229,271,307,331,337,367,379,439, %T A005382 499,547,577,601,607,619,661,691,727,811,829,877,937,967,997,1009, %U A005382 1069,1171,1237,1279,1297,1399,1429,1459,1531,1609,1627,1657,1759,1867,2011 %N A005382 Primes p such that 2p-1 is also prime. %C A005382 Sequence gives values of p such Sum_{i=1..p} gcd(p,i) = A018804(p) is prime. - _Benoit Cloitre_, Jan 25 2002 %C A005382 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 %C A005382 Primes in A006254. - _Zak Seidov_, Mar 26 2013 %C A005382 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 %D A005382 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence). %H A005382 T. D. Noe, Table of n, a(n) for n = 1..10000 %H A005382 M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972, p. 870. %H A005382 R. P. Boas & N. J. A. Sloane, Correspondence, 1974 %H A005382 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. %H A005382 Marius Tărnăuceanu, Arithmetic progressions in finite groups, arXiv:2003.10060 [math.GR], 2020. %H A005382 Wikipedia, Cunningham chain %F A005382 a(n) = A129521(n) / A005383(n). - _Reinhard Zumkeller_, Apr 19 2007 %F A005382 a(n) = (A005383(n) + 1)/2. - _Zak Seidov_, Nov 04 2010 %p A005382 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); %t A005382 Select[Prime[Range[300]], PrimeQ[2#-1]&] %o A005382 (Magma) [n: n in [0..1000] | IsPrime(n) and IsPrime(2*n-1)] // _Vincenzo Librandi_, Nov 18 2010 %o A005382 (PARI) select(p->isprime(2*p-1),primes(500)) \\ _Charles R Greathouse IV_, Apr 26 2012 %o A005382 (Haskell) %o A005382 a005382 n = a005382_list !! (n-1) %o A005382 a005382_list = filter %o A005382 ((== 1) . a010051 . (subtract 1) . (* 2)) a000040_list %o A005382 -- _Reinhard Zumkeller_, Oct 03 2012 %o A005382 (PARI) forprime(n=2, 10^3, if(ispseudoprime(2*n-1), print1(n, ", "))) \\ _Felix Fröhlich_, Jun 15 2014 %Y A005382 Cf. A005383, A005384 (2p+1), A057326, A057327, A057328, A057329, A057330, A005603, A063908 (2p-3), A063909 (2p-5), A023204 (2p+3), A000384, A001358. %Y A005382 Cf. A010051, A000040, A053685 (subsequence), A006254. %K A005382 nonn,easy %O A005382 1,1 %A A005382 _N. J. A. Sloane_ # Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE