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 A005939 Pseudoprimes to base 10. (Formerly M4612) 11

%I M4612

%S 9,33,91,99,259,451,481,561,657,703,909,1233,1729,2409,2821,2981,3333,

%T 3367,4141,4187,4521,5461,6533,6541,6601,7107,7471,7777,8149,8401,

%U 8911,10001,11111,11169,11649,12403,12801,13833,13981,14701,14817,14911,15211

%N Pseudoprimes to base 10.

%C This sequence is a subsequence of A121014 & A121912. In fact the terms are composite terms n of these sequences such that gcd(n,10)=1. Theorem: If both numbers q & 2q-1 are primes(q is in the sequence A005382) and n=q*(2q-1) then 10^(n-1) == 1 (mod n) (n is in the sequence A005939) iff mod(q, 20) is in the set {1, 7, 19}. 91,703,12403,38503,79003,188191,269011,... are such terms. - _Farideh Firoozbakht_, Sep 15 2006

%C Composite numbers n such that 10^(n-1) == 1 (mod n). - _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 T. D. Noe, <a href="/A005939/b005939.txt">Table of n, a(n) for n = 1..1000</a>

%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[15300], ! PrimeQ[ # ] && PowerMod[10, (# - 1), # ] == 1 &] (* _Farideh Firoozbakht_, Sep 15 2006 *)

%Y Cf. A001567 (pseudoprimes to base 2), A005382, A121014, A121912.

%K nonn

%O 1,1

%A _N. J. A. Sloane_

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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.)