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

Author

Farideh Firoozbakht, Sep 12 2006

Keywords

• easy
• nonn

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.

Examples

			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)
		

Links

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

Crossrefs

Cf. A005937.

Programs

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 *)

Extensions

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