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A246120

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

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

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OFFSET

0,1

COMMENTS

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 sequence is a subset of A205506 with only m=3^n, which is similar to A153438.

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

LINKS

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

FORMULA

a(n) = A085398(2*3^(n+1)). - Jinyuan Wang, Jan 01 2023

EXAMPLE

When k = 7, k^18 - k^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)