A046025 Numbers k such that 6*k+1, 12*k+1 and 18*k+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

Author

Eric W. Weisstein

Keywords

• nonn

Comments

Main entry for this sequence is A033502.

k is a Carmichael number generator giving C(k) = (6*k+1)*(12*k+1)*(18*k+1) = A382809(k).

References

• R. K. Guy, Unsolved Problems in Number Theory, A13.
• 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.
• Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See p. 101.

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.

Crossrefs

Cf. A033502, A002997, A382809.

Programs

Mathematica

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

PARI

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

Extensions

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