login
Numbers of the form p*q, p and q prime with q=2*p-1.
22

%I #68 Oct 21 2024 04:46:41

%S 6,15,91,703,1891,2701,12403,18721,38503,49141,79003,88831,104653,

%T 146611,188191,218791,226801,269011,286903,385003,497503,597871,

%U 665281,721801,736291,765703,873181,954271,1056331,1314631,1373653,1537381

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

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

%H David W. Wilson, <a href="/A129521/b129521.txt">Table of n, a(n) for n = 1..1000</a>

%H D. E. Iannucci, <a href="http://math.colgate.edu/~integers/s77/s77.Abstract.html">When the small divisors of a natural number are in arithmetic progression</a>, INTEGERS, Electronic Journal of Combinatorial Number Theory, #77, 2018. See p. 9.

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

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

%o (Magma) [2*n^2-n: n in [0..1000]|IsPrime(n) and IsPrime(2*n-1)]; // _Vincenzo Librandi_, Dec 27 2010

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

%o (Haskell)

%o a129521 n = p * (2 * p - 1) where p = a005382 n

%o -- _Reinhard Zumkeller_, Nov 10 2013

%Y Cf. A005382, A005383.

%Y Subsequence of A006881, A129510, and A122781.

%Y Intersection of A000384 and A001358, "hexagonal semiprimes". - _Wesley Ivan Hurt_, Jul 04 2013

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

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Apr 19 2007