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A290810 Numbers n such that 6n-1, 12n-1 and 18n-1 are all primes. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

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

LINKS

Table of n, a(n) for n=1..51.

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

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Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)