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 A005937 Pseudoprimes to base 6. (Formerly M5246) 11

%I M5246

%S 35,185,217,301,481,1105,1111,1261,1333,1729,2465,2701,2821,3421,3565,

%T 3589,3913,4123,4495,5713,6533,6601,8029,8365,8911,9331,9881,10585,

%U 10621,11041,11137,12209,14315,14701,15841,16589,17329,18361,18721

%N Pseudoprimes to base 6.

%C Theorem: If both numbers q and 2q-1 are primes and n=q*(2q-1) then 6^(n-1) == 1 (mod n) (n is in the sequence) iff q is of the form 12k+1. 2701, 18721, 49141, 104653, 226801, 665281, ... are such terms. This sequence is a subsequence of A122783. - _Farideh Firoozbakht_, Sep 12 2006

%C Composite numbers k such that 6^(k-1) == 1 (mod k). - _Michel Lagneau_, Feb 18 2012

%D R. K. Guy, Unsolved Problems in Number Theory, A12.

%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

%H R. J. Mathar, T. D. Noe, and Charles R Greathouse IV, <a href="/A005937/b005937.txt">Table of n, a(n) for n = 1..10000</a> (Mathar 1..118, Noe 119..1000, Greathouse 1001..10000)

%H C. Pomerance & N. J. A. Sloane, <a href="/A001567/a001567_4.pdf">Correspondence, 1991</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t Select[Range[20000], ! PrimeQ[ # ] && PowerMod[6, #-1, # ] == 1 &] (* _Farideh Firoozbakht_, Sep 12 2006 *)

%Y Cf. A001567 (pseudoprimes to base 2), A122783.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

%E More terms from _Farideh Firoozbakht_, Sep 12 2006

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Last modified August 18 04:47 EDT 2022. Contains 356204 sequences. (Running on oeis4.)