%I #12 Mar 13 2020 11:56:08

%S 1,4,5,14,15,29,39,40,49,70,110,159,169,204,235,260,264,315,334,355,

%T 390,425,449,490,560,565,599,634,725,729,735,820,824,889,1019,1029,

%U 1349,1379,1419,1510,1580,1590,1694,1719,1765,1925,1930,1950,1985,2044,2150

%N Numbers k such that 6k-1, 12k-1 and 18k-1 are all primes.

%C If k is in the sequence then (6k-1)(12k-1)(18k-1) = 36k * (36k^2 - 11k + 1) - 1 is a Lucas-Carmichael number (A006972).

%C Analogous to A046025 as A006972 (Lucas-Carmichael numbers) is analogous to A002997 (Carmichael numbers).

%H Daniel Starodubtsev, <a href="/A290810/b290810.txt">Table of n, a(n) for n = 1..10000</a>

%F 6*a(n) - 1 = A067256(n+1).

%e 1 is in the sequence since 6*1 - 1 = 5, 12*1 - 1 = 11 and 18*1 - 1 = 17 are all primes, and 5*11*17 = 935 is a Lucas-Carmichael number.

%t seq = {}; Do[ If[ AllTrue[{6 m - 1, 12 m - 1, 18 m - 1}, PrimeQ ], AppendTo[seq, m] ], {m, 1, 10^5} ]; seq

%o (PARI) isok(n) = isprime(6*n-1) && isprime(12*n-1) && isprime(18*n-1); \\ _Michel Marcus_, Aug 11 2017

%Y Cf. A002997, A006972, A046025, A067256, A087788, A216925.

%Y Intersection of A024898, A138620 and A138918.

%K nonn

%O 1,2

%A _Amiram Eldar_, Aug 11 2017