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
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) = (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[300]], 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
KEYWORD
nonn,easy
AUTHOR
STATUS
approved