A122783 Nonprimes k > 0 such that 6^k==6 (mod k).

1, 6, 10, 15, 21, 30, 35, 105, 185, 190, 217, 231, 301, 430, 435, 481, 561, 777, 1105, 1111, 1221, 1261, 1333, 1729, 1866, 2121, 2465, 2553, 2701, 2821, 2955, 3421, 3565, 3589, 3885, 3913, 4123, 4495, 5061, 5565, 5662, 5713, 6531, 6533, 6601

Offset

1,2

Comments

Theorem: If both numbers q and 2q-1 are primes then n=q*(2q-1) is in the sequence iff q<5 or q is of the form 12k+1. 6,15,2701,18721,49141,104653,226801,665281,... are such terms.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

1 is a term since 6^1 = 6 is congruent to 6 mod 1.
2 is not a term since although 6^2 === 6 (mod 2), 2 IS a prime.
4 is not a term since 6^4 = 1296 == 0 mod 4, while 6 == 2 (mod 4).
6 is a term since 6^6 = 46656 == 0 (mod 6), and 6 == 0 (mod 6).
10 is a term because 6^10 = 60466176 == 6 (mod 10)

Mathematica

Select[Range[7000], ! PrimeQ[ # ] && Mod[6^#, # ] == Mod[6, # ] &]
Join[{1, 6}, Select[Range[7000], !PrimeQ[#]&&PowerMod[6, #, #]==6&]] (* Harvey P. Dale, Jan 06 2022 *)

Crossrefs

Cf. A005937.

Sequence in context: A115744 A211007 A315279 * A333747 A124000 A229321

Adjacent sequences: A122780 A122781 A122782 * A122784 A122785 A122786

Keyword

easy,nonn

Author

Farideh Firoozbakht, Sep 12 2006

Extensions

Examples added by N. J. A. Sloane, Jan 06 2022

Status

approved