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A290811 Numbers n such that (6n-1, 6n+1), (12n-1, 12n+1) and (18n-1, 18n+1) are 3 pairs of twin primes. 1
1, 8925, 70070, 70385, 270725, 355040, 566650, 866635, 874335, 1091545, 1230740, 1295980, 1586095, 1594285, 1738380, 1974210, 2201325, 2427145, 2436665, 3124660, 3349990, 3599470, 3661350, 4059825, 4101790, 4486020, 4726540, 5139680, 5613370, 5898655, 6279035 (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) is a Carmichael number (A002997) and (6n-1)*(12n-1)*(18n-1) is a Lucas-Carmichael number (A006972).

Intersection of A046025 and A290810.

The first 10 pairs of corresponding Lucas-Carmichael and Carmichael numbers ((6n-1)*(12n-1)*(18n-1), (6n+1)*(12n+1)*(18n+1)) are:

(935, 1729)

(921329139943799, 921392227198801)

(445860973748310119, 445864862313790921)

(451901165073782759, 451905088679976961)

(25715181770344848599, 25715239817629143601)

(58001133699332691839, 58001233533626759041)

(235803065459494289399, 235803319764534509401)

(843555229160685647759, 843555823997214441961)

(866240412591524160959, 866241018045184403161)

(1685504102154302331719, 1685505045798928055521)

(2416038446298343361039, 2416039645957333860241)

LINKS

Tim Johannes Ohrtmann, Table of n, a(n) for n = 1..10000

EXAMPLE

1 is in the sequence since (6*1 - 1, 6*1 + 1) = (5, 7), (12*1 - 1, 12*1 + 1) = (11, 13) and (18*1 - 1, 18*1 + 1) = (17, 19) are all pairs of twin primes.

MATHEMATICA

seq = {}; Do[ If[ AllTrue[{6 m - 1, 6 m + 1, 12 m - 1, 12 m + 1, 18 m - 1,

    18 m + 1}, PrimeQ ], AppendTo[seq, m]], {m, 1, 10^7} ]; seq

PROG

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

CROSSREFS

Cf. A002997, A006972, A033502, A046025, A290810.

Sequence in context: A256237 A065235 A087167 * A259631 A251921 A217604

Adjacent sequences:  A290808 A290809 A290810 * A290812 A290813 A290814

KEYWORD

nonn

AUTHOR

Amiram Eldar, Aug 11 2017

STATUS

approved

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Last modified October 19 04:40 EDT 2019. Contains 328211 sequences. (Running on oeis4.)