

A067256


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


12



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
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OFFSET

1,1


COMMENTS

a(n)*(2a(n)+1)*(3a(n)+2) are LucasCarmichael numbers for n > 1. Analogous to A174734 as A006972 (LucasCarmichael 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



