|
%I #20 Jun 24 2019 11:40:57
%S 380,506,3796,6006,8976,9186,10920,12896,14476,14800,15386,32326,
%T 38460,39536,40420,41456,43430,60076,74676,76986,82530,87390,99486,
%U 107926,112840,126996,127920,144326,179566,181986,188526,193006,194616,205200,217520,230370
%N Even numbers k such that 6k+1, 12k+1, 18k+1, 36k+1 and 72k+1 are all primes.
%C (6n+1)*(12n+1)*(18n+1)*(36n+1)*(72n+1) is a Carmichael number for all n in this sequence.
%C More precisely, these products are in A112428 = A002997 intersect A014614. - _M. F. Hasler_, Apr 14 2015
%H Amiram Eldar, <a href="/A206349/b206349.txt">Table of n, a(n) for n = 1..10000</a>
%H Jack Chernick, <a href="https://doi.org/10.1090/S0002-9904-1939-06953-X">On Fermat's simple theorem</a>, Bull. Amer. Math. Soc., Volume 45, Number 4 (1939), pp. 269-274.
%t Select[Range[250000], PrimeQ[6 #+1] && PrimeQ[12 #+1] && PrimeQ[18 #+1] && PrimeQ[36 #+1] && PrimeQ[72 #+1] && Mod[#,2] == 0&]
%o (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
%K nonn,easy
%O 1,1
%A _José María Grau Ribas_, Feb 06 2012
|
