A206349 Even numbers k such that 6k+1, 12k+1, 18k+1, 36k+1 and 72k+1 are all primes.

380, 506, 3796, 6006, 8976, 9186, 10920, 12896, 14476, 14800, 15386, 32326, 38460, 39536, 40420, 41456, 43430, 60076, 74676, 76986, 82530, 87390, 99486, 107926, 112840, 126996, 127920, 144326, 179566, 181986, 188526, 193006, 194616, 205200, 217520, 230370

Offset

1,1

Comments

(6n+1)*(12n+1)*(18n+1)*(36n+1)*(72n+1) is a Carmichael number for all n in this sequence.

More precisely, these products are in A112428 = A002997 intersect A014614. - M. F. Hasler, Apr 14 2015

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Jack Chernick, On Fermat's simple theorem, Bull. Amer. Math. Soc., Volume 45, Number 4 (1939), pp. 269-274.

Mathematica

Select[Range[250000], PrimeQ[6 #+1] && PrimeQ[12 #+1] && PrimeQ[18 #+1] && PrimeQ[36 #+1] && PrimeQ[72 #+1] && Mod[#, 2] == 0&]

Prog

(PARI) is_A206349(n, c=72)=!bittest(n, 0)&&!until(bittest(c\=2, 0)&&9>c+=3, isprime(n*c+1)||return) \\ M. F. Hasler, Apr 14 2015

Crossrefs

Sequence in context: A027503 A340200 A099728 * A252130 A252123 A158597

Adjacent sequences: A206346 A206347 A206348 * A206350 A206351 A206352

Keyword

nonn,easy

Author

José María Grau Ribas, Feb 06 2012

Status

approved