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

1,2

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.

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 *)

Prog

(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
(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
(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

Crossrefs

Cf. A002997, A046025, A206349, A257035.

Sequence in context: A119204 A119206 A060463 * A151743 A348923 A348922

Adjacent sequences: A206021 A206022 A206023 * A206025 A206026 A206027

Keyword

nonn

Author

José María Grau Ribas, Feb 03 2012

Status

approved