A129521 Numbers of the form p*q, p and q prime with q=2*p-1.

6, 15, 91, 703, 1891, 2701, 12403, 18721, 38503, 49141, 79003, 88831, 104653, 146611, 188191, 218791, 226801, 269011, 286903, 385003, 497503, 597871, 665281, 721801, 736291, 765703, 873181, 954271, 1056331, 1314631, 1373653, 1537381

Offset: 1

Author

Reinhard Zumkeller, Apr 19 2007

Keywords

• nonn

Comments

All terms are Fermat 4-pseudoprimes, i.e., satisfy 4^n == 4 (mod n). See A020136 and A122781.

Links

• David W. Wilson, Table of n, a(n) for n = 1..1000
• D. E. Iannucci, When the small divisors of a natural number are in arithmetic progression, INTEGERS, Electronic Journal of Combinatorial Number Theory, #77, 2018. See p. 9.

Crossrefs

Cf. A005382, A005383.

Subsequence of A006881, A129510, and A122781.

Intersection of A000384 and A001358, "hexagonal semiprimes". - Wesley Ivan Hurt, Jul 04 2013

Cf. A141768, A191311, A191592, A245365, A259676, A259677.

Programs

Haskell

a129521 n = p * (2 * p - 1) where p = a005382 n
-- Reinhard Zumkeller, Nov 10 2013

Magma

[2*n^2-n: n in [0..1000]|IsPrime(n) and IsPrime(2*n-1)]; // Vincenzo Librandi, Dec 27 2010

Mathematica

p = Select[Prime[Range[155]], PrimeQ[2# - 1] &]; p (2p - 1) (* Robert G. Wilson v, Sep 11 2011 *)

PARI

forprime(p=2,10000,q=2*p-1;if(isprime(q),print1(p*q,", ")))

Formula

a(n) = A005382(n)*A005383(n).