A067256 Numbers n such that n, 2n+1, 3n+2 are primes.

3, 5, 23, 29, 83, 89, 173, 233, 239, 293, 419, 659, 953, 1013, 1223, 1409, 1559, 1583, 1889, 2003, 2129, 2339, 2549, 2693, 2939, 3359, 3389, 3593, 3803, 4349, 4373, 4409, 4919, 4943, 5333, 6113, 6173, 8093, 8273, 8513, 9059, 9479, 9539, 10163, 10313

Offset: 1

Author

Benoit Cloitre, Feb 20 2002

Keywords

• nonn

Comments

a(n)*(2a(n)+1)*(3a(n)+2) are Lucas-Carmichael numbers for n > 1. Analogous to A174734 as A006972 (Lucas-Carmichael numbers) is analogous to A002997 (Carmichael numbers). - Amiram Eldar, Aug 11 2017

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A005384, A006972, A067257, A067258, A101767, A101768, A101769, A101770, A174734, A216925.

Programs

Magma

[n: n in [1..15000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2)]; // Vincenzo Librandi, Oct 31 2014

Mathematica

Select[Prime[Range[10^4]],PrimeQ[2*#+1]&&PrimeQ[3*#+2] &] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2008 *)

PARI

is(n)=isprime(3*n+2) && isprime(2*n+1) && isprime(n) \\ Charles R Greathouse IV, Sep 14 2015