

A005939


Pseudoprimes to base 10.
(Formerly M4612)


12



9, 33, 91, 99, 259, 451, 481, 561, 657, 703, 909, 1233, 1729, 2409, 2821, 2981, 3333, 3367, 4141, 4187, 4521, 5461, 6533, 6541, 6601, 7107, 7471, 7777, 8149, 8401, 8911, 10001, 11111, 11169, 11649, 12403, 12801, 13833, 13981, 14701, 14817, 14911, 15211
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

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 & 2q1 are primes(q is in the sequence A005382) and n=q*(2q1) then 10^(n1) == 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
Composite numbers n such that 10^(n1) == 1 (mod n).  Michel Lagneau, Feb 18 2012


REFERENCES

R. K. Guy, Unsolved Problems in Number Theory, A12.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000
C. Pomerance & N. J. A. Sloane, Correspondence, 1991
Index entries for sequences related to pseudoprimes


MATHEMATICA

Select[Range[15300], ! PrimeQ[ # ] && PowerMod[10, (#  1), # ] == 1 &] (* Farideh Firoozbakht, Sep 15 2006 *)


CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A121014, A121912.
Sequence in context: A146171 A146188 A020228 * A020326 A201024 A228170
Adjacent sequences: A005936 A005937 A005938 * A005940 A005941 A005942


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


STATUS

approved



