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

Author

José María Grau Ribas, Feb 06 2012

Keywords

• nonn
• easy

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.

Programs

Mathematica

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

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