A114245 Number of Fermat pseudoprimes to base 3 less than 10^n.

0, 1, 6, 23, 78, 246, 760, 2155, 5804, 15472, 39871, 102839, 264461

Offset

1,3

Links

Table of n, a(n) for n=1..13.

Michal Mikuš, Computing the Pseudoprimes up to 10^13, Cybernetics and Informatics, International Conference SSKI, February 10-13, 2010.

Eric Weisstein's World of Mathematics, Fermat Pseudoprime.

Index entries for sequences related to pseudoprimes.

Formula

A005935(a(n)) < 10^n; A005935(a(n)+1) > 10^n. - R. J. Mathar, Feb 10 2007

Mathematica

Table[Count[Select[Range[2, 10^6], ! PrimeQ[#] && PowerMod[3, # - 1, #] == 1 &], x_ /; x < 10^n], {n, 6}]  (* Robert Price, Jun 09 2019 *)

Prog

(PARI) isFps(n, b)= { if(isprime(n), return(0) ) ; if( (b^(n-1)) % n == 1, return(1), return(0) ) ; } { a=0 ; e=1 ; for(n=1, 10^12, if( n == 10^e, e++ ; print(a) ; ) ; a += isFps(n, 3) ; ) ; } \\ R. J. Mathar, Feb 10 2007

Crossrefs

Cf. A005935, A114247, A114249.

Sequence in context: A058751 A034359 A220148 * A220238 A078798 A027043

Adjacent sequences: A114242 A114243 A114244 * A114246 A114247 A114248

Keyword

nonn,more

Author

Eric W. Weisstein, Nov 18 2005

Extensions

a(9)-a(10) from Washington Bomfim, Mar 02 2012

a(11)-a(12) from Hiroaki Yamanouchi, Sep 25 2015

a(13) from Mikuš (2010) added by Amiram Eldar, Mar 31 2024

Status

approved