

A005935


Pseudoprimes to base 3.
(Formerly M5362)


17



91, 121, 286, 671, 703, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7381, 8401, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345, 23521, 24046, 24661, 24727, 28009, 29161
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OFFSET

1,1


COMMENTS

Theorem: If q>3 and both numbers q and (2q1) are primes then n=q*(2q1) is a pseudoprime to base 3 (i.e. n is in the sequence). So for n>2, A005382(n)*(2*A005382(n)1) is in the sequence (see Comments lines for the sequence A122780). 91,703,1891,2701,12403,18721,38503,49141... are such terms. This sequence is a subsequence of A122780.  Farideh Firoozbakht, Sep 13 2006
Composite numbers n such that 3^(n1) == 1 (mod n).


REFERENCES

J.M. De Koninck, Ces nombres qui nous fascinent, Entry 91, p. 33, Ellipses, Paris 2008.
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

R. J. Mathar and T. D. Noe, Table of n, a(n) for n = 1..1000 (R. J. Mathar to 798 terms)
J. Bernheiden, Pseudoprimes (Text in German)
F. Richman, Primality testing with Fermat's little theorem
Eric Weisstein's World of Mathematics, Fermat Pseudoprime
Index entries for sequences related to pseudoprimes


MATHEMATICA

base = 3; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n1, n] == 1, AppendTo[t, n]]]; t (* T. D. Noe, Feb 21 2012 *)


PROG

(PARI) is_A005935(n)={Mod(3, n)^(n1)==1 & !ispseudoprime(n) & n>1} \\  M. F. Hasler, Jul 19 2012


CROSSREFS

Cf. A001567 (pseudoprimes to base 2), A005382, A122780.
Sequence in context: A236845 A157345 A092125 * A020307 A020235 A046427
Adjacent sequences: A005932 A005933 A005934 * A005936 A005937 A005938


KEYWORD

nonn


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from David W. Wilson, Aug 15 1996.


STATUS

approved



