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!)
A246120 Least k such that k^(3^n)*(k^(3^n)-1)+1 is prime. 4

%I

%S 2,6,7,93,15,372,421,759,7426,9087

%N Least k such that k^(3^n)*(k^(3^n)-1)+1 is prime.

%C Numbers of the form k^m*(k^m-1)+1 with m > 0, k > 1 may be primes only if m is 3-smooth, because these numbers are Phi(6,k^m) and cyclotomic factorizations apply to any prime divisors >3. This series is a subset of A205506 with only m=3^n, which is similar to the A153438 series.

%C Search limits: a(10) > 35000, a(11) > 3500.

%e When k = 7, k^18-k^9+1 is prime. Since this isn't prime for k < 7, a(2) = 7.

%t a246120[n_Integer] := Module[{k = 1},

%t While[! PrimeQ[k^(3^n)*(k^(3^n) - 1) + 1], k++]; k]; a246120 /@ Range[0, 9] (* _Michael De Vlieger_, Aug 15 2014 *)

%o (PARI)

%o a(n)=k=1;while(!ispseudoprime(k^(3^n)*(k^(3^n)-1)+1),k++);k

%o n=0;while(n<100,print1(a(n),", ");n++) \\ _Derek Orr_, Aug 14 2014

%Y Cf. A205506, A246119, A246121, A153438, A101406, A153436, A056993.

%K nonn,more,hard

%O 0,1

%A _Serge Batalov_, Aug 14 2014

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 8 01:41 EST 2021. Contains 341934 sequences. (Running on oeis4.)