A206024 Numbers k such that 6k+1, 12k+1, 18k+1 and 36k+1 are all primes.

1, 45, 56, 121, 206, 255, 380, 506, 511, 710, 871, 1025, 1421, 1515, 1696, 2191, 2571, 2656, 2681, 3341, 3566, 3741, 3796, 3916, 3976, 4235, 4340, 4426, 5645, 5875, 6006, 7066, 7616, 7826, 7976, 8900, 8925, 8976, 9025, 9186, 9600, 9761, 10920, 11301, 11385

Offset: 1

Author

José María Grau Ribas, Feb 03 2012

Keywords

• nonn

Comments

(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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..5000 from Muniru A Asiru)
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Cf. A002997, A046025, A206349, A257035.

Programs

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

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

Maple

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

Mathematica

Select[Range[20000], PrimeQ[6 # + 1] && PrimeQ[12 # + 1] && PrimeQ[18 # + 1] && PrimeQ[36 # + 1] &]
Select[Range[12000],And@@PrimeQ[{6,12,18,36}#+1]&] (* Harvey P. Dale, Mar 25 2013 *)

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

PARI

is(m,c=36)=!until(bittest(c\=2,0)&&9>c+=3, isprime(m*c+1)||return) \\ M. F. Hasler, Apr 15 2015