%I #35 Apr 22 2024 04:06:25
%S 1,45,56,121,206,255,380,506,511,710,871,1025,1421,1515,1696,2191,
%T 2571,2656,2681,3341,3566,3741,3796,3916,3976,4235,4340,4426,5645,
%U 5875,6006,7066,7616,7826,7976,8900,8925,8976,9025,9186,9600,9761,10920,11301,11385
%N Numbers k such that 6k+1, 12k+1, 18k+1 and 36k+1 are all primes.
%C (6k+1)*(12k+1)*(18k+1)*(36k+1) is a Carmichael number for all k in this sequence. - _José María Grau Ribas_, Feb 06 2012
%H Amiram Eldar, <a href="/A206024/b206024.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..5000 from Muniru A Asiru)
%H <a href="/index/Ca#Carmichael">Index entries for sequences related to Carmichael numbers</a>.
%p select(n->isprime(6*n+1) and isprime(12*n+1) and isprime(18*n+1) and isprime(36*n+1),[$1..12000]); # _Muniru A Asiru_, May 27 2018
%t Select[Range[20000], PrimeQ[6 # + 1] && PrimeQ[12 # + 1] && PrimeQ[18 # + 1] && PrimeQ[36 # + 1] &]
%t Select[Range[12000],And@@PrimeQ[{6,12,18,36}#+1]&] (* _Harvey P. Dale_, Mar 25 2013 *)
%o (PARI) forprime(p=2,1e5,if(p%6!=1,next);if(isprime(2*p-1)&&isprime(3*p-2)&&isprime(6*p-5),print1(p\6", "))) \\ _Charles R Greathouse IV_, Feb 06 2012
%o (PARI) is(m,c=36)=!until(bittest(c\=2,0)&&9>c+=3, isprime(m*c+1)||return) \\ _M. F. Hasler_, Apr 15 2015
%o (Magma) [n: n in [0..2*10^4] | IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and IsPrime(36*n+1)]; // _Vincenzo Librandi_, Apr 15 2015
%o (GAP) Filtered([1..12000],n->IsPrime(6*n+1) and IsPrime(12*n+1) and IsPrime(18*n+1) and IsPrime(36*n+1)); # _Muniru A Asiru_, May 27 2018
%Y Cf. A002997, A046025, A206349, A257035.
%K nonn
%O 1,2
%A _José María Grau Ribas_, Feb 03 2012