

A246120


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


4




OFFSET

0,1


COMMENTS

Numbers of the form k^m*(k^m1)+1 with m > 0, k > 1 may be primes only if m is 3smooth, 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.
Search limits: a(10) > 35000, a(11) > 3500.


LINKS

Table of n, a(n) for n=0..9.


EXAMPLE

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


MATHEMATICA

a246120[n_Integer] := Module[{k = 1},
While[! PrimeQ[k^(3^n)*(k^(3^n)  1) + 1], k++]; k]; a246120 /@ Range[0, 9] (* Michael De Vlieger, Aug 15 2014 *)


PROG

(PARI)
a(n)=k=1; while(!ispseudoprime(k^(3^n)*(k^(3^n)1)+1), k++); k
n=0; while(n<100, print1(a(n), ", "); n++) \\ Derek Orr, Aug 14 2014


CROSSREFS

Cf. A205506, A246119, A246121, A153438, A101406, A153436, A056993.
Sequence in context: A216037 A250547 A057249 * A300659 A155003 A327279
Adjacent sequences: A246117 A246118 A246119 * A246121 A246122 A246123


KEYWORD

nonn,more,hard


AUTHOR

Serge Batalov, Aug 14 2014


STATUS

approved



