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

1,1

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

Mathematica

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

Prog

(Magma) [n: n in [1..15000] | IsPrime(n) and IsPrime(2*n+1) and IsPrime(3*n+2)]; // Vincenzo Librandi, Oct 31 2014
(PARI) is(n)=isprime(3*n+2) && isprime(2*n+1) && isprime(n) \\ Charles R Greathouse IV, Sep 14 2015

Crossrefs

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

Sequence in context: A137084 A271347 A222424 * A136891 A296920 A106857

Adjacent sequences: A067253 A067254 A067255 * A067257 A067258 A067259

Keyword

nonn

Author

Benoit Cloitre, Feb 20 2002

Status

approved