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A206024
Numbers k such that 6k+1, 12k+1, 18k+1 and 36k+1 are all primes.
6
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
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
KEYWORD
nonn
AUTHOR
STATUS
approved