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