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A246120 Least k such that k^(3^n)*(k^(3^n)-1)+1 is prime. 4
2, 6, 7, 93, 15, 372, 421, 759, 7426, 9087 (list; graph; refs; listen; history; text; internal format)
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 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^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)

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

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Last modified January 17 03:14 EST 2021. Contains 340214 sequences. (Running on oeis4.)