The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A268081 Least positive integer k such that 3^n-1 and k^n-1 are relatively prime. 1

%I #15 Mar 13 2020 16:55:52

%S 2,2,2,10,2,28,2,10,2,22,10,910,2,2,2,170,2,3458,2,110,2,46,10,910,2,

%T 2,2,290,2,9548,2,340,10,2,22,639730,2,2,2,4510,2,1204,10,230,2,94,2,

%U 216580,2,22,2,530,2,3458,22,580,2,118,2,18928910

%N Least positive integer k such that 3^n-1 and k^n-1 are relatively prime.

%C Note that (3^n-1)^n-1 is always relatively prime to 3^n-1.

%C According to the conjecture given in A086892, a(n) = 2 infinitely often.

%C When n>1, a(n) = 2 if and only if A260119(n) = 3.

%e Since 3^5-1 = 242 and 2^5-1 = 31 are relatively prime, a(5) = 3.

%t Table[k = 1; While[! CoprimeQ[3^n - 1, k^n - 1], k++]; k, {n, 59}] (* _Michael De Vlieger_, Jan 27 2016 *)

%o (Sage)

%o def min_k(n):

%o g, k=2, 0

%o while g!=1:

%o k=k+1

%o g=gcd(3^n-1, k^n-1)

%o return k

%o print([min_k(n) for n in [1..60]])

%o (PARI) a(n) = {k=1; while( gcd(3^n-1, k^n-1)!=1, k++); k; }

%Y Cf. A086892, A260119.

%K nonn

%O 1,1

%A _Tom Edgar_, Jan 25 2016

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 04:02 EDT 2024. Contains 372900 sequences. (Running on oeis4.)