A290810 Numbers k such that 6k-1, 12k-1 and 18k-1 are all primes.

1, 4, 5, 14, 15, 29, 39, 40, 49, 70, 110, 159, 169, 204, 235, 260, 264, 315, 334, 355, 390, 425, 449, 490, 560, 565, 599, 634, 725, 729, 735, 820, 824, 889, 1019, 1029, 1349, 1379, 1419, 1510, 1580, 1590, 1694, 1719, 1765, 1925, 1930, 1950, 1985, 2044, 2150

Offset

1,2

Comments

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).

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

Links

Daniel Starodubtsev, Table of n, a(n) for n = 1..10000

Formula

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

Example

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.

Mathematica

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

Prog

(PARI) isok(n) = isprime(6*n-1) && isprime(12*n-1) && isprime(18*n-1); \\ Michel Marcus, Aug 11 2017

Crossrefs

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

Intersection of A024898, A138620 and A138918.

Sequence in context: A238315 A091311 A008540 * A000867 A191142 A049770

Adjacent sequences: A290807 A290808 A290809 * A290811 A290812 A290813

Keyword

nonn

Author

Amiram Eldar, Aug 11 2017

Status

approved