A046025 Numbers n such that 6n+1, 12n+1 and 18n+1 are all primes.

1, 6, 35, 45, 51, 55, 56, 100, 121, 195, 206, 216, 255, 276, 370, 380, 426, 506, 510, 511, 710, 741, 800, 825, 871, 930, 975, 1025, 1060, 1115, 1140, 1161, 1270, 1280, 1281, 1311, 1336, 1361, 1365, 1381, 1420, 1421, 1441, 1490, 1515, 1696, 1805, 1875, 1885

Offset

1,2

Comments

Main entry for this sequence is A033502.

n is a Carmichael number generator giving C(n) = (6n+1)(12n+1)(18n+1).

References

Ivan Niven, Herbert S. Zuckerman and Hugh L. Montgomery, An Introduction to the Theory Of Numbers, Fifth Edition, Wiley NY 1991, page 83, problem #20.

R. K. Guy, Unsolved Problems in Number Theory, A13.

Links

Donovan Johnson, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Carmichael Number.

Index entries for sequences related to Carmichael numbers.

Mathematica

Select[Range[2000], And@@PrimeQ[{6, 12, 18}#+1]&] (* Harvey P. Dale, May 26 2014 *)

Prog

(PARI) is(n)=isprime(6*n+1) && isprime(12*n+1) && isprime(18*n+1) \\ Charles R Greathouse IV, Jan 04 2022

Crossrefs

Cf. A033502, A002997.

Sequence in context: A209182 A275407 A362306 * A198327 A009583 A369351

Adjacent sequences: A046022 A046023 A046024 * A046026 A046027 A046028

Keyword

nonn

Author

Eric W. Weisstein

Extensions

Better description from Robert G. Wilson v, Sep 27 2000

Status

approved