login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A086250 Smallest base-2 Fermat pseudoprime x that has ord(2,x) = n, or 0 if one does not exist. 2
0, 0, 0, 0, 0, 0, 0, 0, 0, 341, 2047, 0, 0, 5461, 4681, 4369, 0, 1387, 0, 13981, 42799, 15709, 8388607, 1105, 1082401, 22369621, 0, 645, 256999, 10261, 0, 16843009, 1227133513, 5726623061, 8727391, 1729, 137438953471, 91625968981, 647089, 561 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,10

COMMENTS

A base-2 Fermat pseudoprime is a composite number x such that 2^x == 2 (mod x). For such an x, ord(2,x) is the smallest positive integer m such that 2^m == 1 (mod x). For a number x to have order n, it must be a factor of 2^n-1 and not be a factor of 2^r-1 for r<n. Sequence A086249 lists the number of pseudoprimes of order n.

LINKS

Max Alekseyev, Table of n, a(n) for n = 1..200

R. G. E. Pinch, Pseudoprimes and their factors (FTP)

Eric Weisstein's World of Mathematics, Pseudoprime

EXAMPLE

a(10) = 1 there is only 1 pseudoprime, 341 = 11*31, having order 10; that is, 2^10 = 1 mod 341.

MATHEMATICA

Table[d=Divisors[2^n-1]; num=0; i=1; done=False; While[m=d[[i]]; done=!PrimeQ[m]&&PowerMod[2, m, m]==2&&MultiplicativeOrder[2, m]==n; If[done, num=m]; !done&&i<Length[d], i++ ]; num, {n, 100}]

PROG

(PARI) { a(n) = fordiv(2^n-1, d, if(d>1 && (d-1)%n==0 && !ispseudoprime(d) && znorder(Mod(2, d))==n, return(d)) ); 0 } /* Max Alekseyev, Jan 07 2015 */

CROSSREFS

Cf. A001567 (base-2 pseudoprimes), A086249.

Sequence in context: A087716 A084653 A143688 * A285549 A306310 A210454

Adjacent sequences:  A086247 A086248 A086249 * A086251 A086252 A086253

KEYWORD

hard,nonn

AUTHOR

T. D. Noe, Jul 14 2003

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 03:32 EST 2021. Contains 341732 sequences. (Running on oeis4.)