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, 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

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