A230722 Carmichael numbers of the form (6*k + 1)*(24*k + 1)*(30*k + 1).

126217, 68154001, 1828377001, 3713287801, 27388362001, 32071969801, 63593140801, 113267783377, 122666876401, 193403531401, 227959335001, 246682590001, 910355497801, 1389020532001, 4790779641001, 5367929037001, 6486222838801, 24572944746001

Offset: 1

Author

Arkadiusz Wesolowski, Oct 28 2013

Keywords

• nonn

Comments

These numbers:

- are pseudoprimes to bases 2, 3 and 5;

- do not occur in A097130 (Carmichael numbers that are not == 1 mod 24).

The number (6*k + 1)*(24*k + 1)*(30*k + 1) is in the sequence if:

- k is congruent to 5 mod 10;

- its three factors are all prime.

Links

• Amiram Eldar, 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.
• Index entries for sequences related to pseudoprimes.

Crossrefs

Subsequence of A002997 and of A083737.

Supersequence of A230746.

Programs

Magma

[a : k in [1..1785 by 2] | IsOne(a mod CarmichaelLambda(a)) where a is (6*k+1)*(24*k+1)*(30*k+1)]