A046025 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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