|
| |
|
|
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^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)
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. A056993, A085398, A101406, A153436, A153438, A205506, A246119, A246121.
Sequence in context: A216037 A250547 A057249 * A300659 A155003 A327279
Adjacent sequences: A246117 A246118 A246119 * A246121 A246122 A246123
|
|
|
KEYWORD
|
nonn,more,hard,changed
|
|
|
AUTHOR
|
Serge Batalov, Aug 14 2014
|
|
|
STATUS
|
approved
|
| |
|
|
