A367231 Carmichael numbers k such that the multiplicative order of 2 modulo k is odd.

15841, 52633, 5049001, 68154001, 104852881, 238244041, 382536001, 3215031751, 3863326897, 7211236033, 8214723001, 15462960481, 22008493921, 23000028481, 29392867201, 31708772257, 41217865921, 53125756201, 60518537641, 74190097801, 77874636001, 83828294551, 103387371361

Offset: 1

Author

Amiram Eldar, Nov 11 2023

Keywords

• nonn

Comments

These Carmichael numbers seem to be relatively rare: among the 4279356 Carmichael numbers below 2^64 only 3097 are terms of this sequence.

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (calculated using data from Claude Goutier)
• Claude Goutier, Compressed text file carm10e22.gz containing all the Carmichael numbers up to 10^22.
• Index entries for sequences related to Carmichael numbers.

Crossrefs

Intersection of A002997 and A036259.

Subsequence of A367230.

Cf. A002326, A163956.

Programs

Mathematica

Select[2*Range[3*10^6] + 1, Mod[#, CarmichaelLambda[#]] == 1 && CompositeQ[#] && OddQ[MultiplicativeOrder[2, #]] &]

PARI

is(n) = n > 1 && n % 2 && !isprime(n) && n % lcm(znstar(n)[2]) == 1 && znorder(Mod(2, n)) % 2;