

A122783


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


6



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
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OFFSET

1,2


COMMENTS

Theorem: If both numbers q and 2q1 are primes then n=q*(2q1) 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



