login
Pseudoprimes to base 65.
1

%I #15 Oct 16 2023 09:54:51

%S 4,8,16,28,32,33,64,112,133,232,289,448,511,561,703,1111,1247,1387,

%T 1856,1891,1921,2452,2701,3439,3553,3729,4291,4564,5068,6533,6601,

%U 6697,8321,8911,9537,9709,9808,9809,10681,11077,11584,11647,12754,13213,14981

%N Pseudoprimes to base 65.

%C Composite numbers n such that 65^(n-1) == 1 (mod n).

%H T. D. Noe, <a href="/A020193/b020193.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t base = 65; t = {}; n = 1; While[Length[t] < 100, n++; If[! PrimeQ[n] && PowerMod[base, n-1, n] == 1, AppendTo[t, n]]]; t (* _T. D. Noe_, Feb 21 2012 *)

%t Select[Range[15000],CompositeQ[#]&&PowerMod[65,#-1,#]==1&] (* _Harvey P. Dale_, Oct 16 2023 *)

%Y Cf. A001567 (pseudoprimes to base 2).

%K nonn

%O 1,1

%A _David W. Wilson_