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A255607 Numbers n such that both 4*n+1 and 6*n+1 are primes.

%I A255607 #34 Sep 08 2022 08:46:11
%S A255607 1,3,7,10,13,18,25,27,37,45,58,70,73,87,100,102,105,112,115,135,142,
%T A255607 153,165,168,175,177,192,202,205,213,220,238,255,258,277,282,298,300,
%U A255607 312,322,325,352,357,363,370,373,417,423,447,465,472,475,513,520
%N A255607 Numbers n such that both 4*n+1 and 6*n+1 are primes.
%C A255607 Numbers n such that A033570(2n) is semiprime.
%H A255607 Harvey P. Dale, <a href="/A255607/b255607.txt">Table of n, a(n) for n = 1..1000</a>
%F A255607 a(n) = A130800(n)/2.
%e A255607 10 is in this sequence because 4*10+1=41 and 6*10+1=61 are primes.
%p A255607 A255607:=n->`if`(isprime(4*n+1) and isprime(6*n+1), n, NULL): seq(A255607(n), n=1..600); # _Wesley Ivan Hurt_, Feb 28 2015
%t A255607 Select[Range[600], PrimeQ[4 # + 1] && PrimeQ[6 # + 1] &]
%t A255607 Select[Range[600],AllTrue[{4#,6#}+1,PrimeQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Sep 22 2020 *)
%o A255607 (Magma) [n: n in [1..600] | IsPrime(6*n+1) and IsPrime(4*n+1)];
%o A255607 (PARI) for(n=1,10^3,if(isprime(4*n+1)&&isprime(6*n+1),print1(n,", "))) \\ _Derek Orr_, Mar 01 2015
%o A255607 (PARI) select( is_A255607(n)=isprime(4*n+1)&&isprime(6*n+1), [1..555]) \\ _M. F. Hasler_, Dec 13 2019
%Y A255607 Cf. A001358, A033570, A130800, A186721.
%Y A255607 Cf. A255584: semiprimes of the form (4*n+1)*(6*n+1).
%K A255607 nonn,easy
%O A255607 1,2
%A A255607 _Vincenzo Librandi_, Feb 28 2015