|
| |
|
|
A246121
|
|
Least k such that k^(6^n)*(k^(6^n) - 1) + 1 is prime.
|
|
3
|
| |
|
|
|
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=6^n.
Numbers of this form are Generalized unique primes. a(6) generates a 306477-digit prime.
|
|
|
LINKS
|
Table of n, a(n) for n=0..6.
C. Caldwell, Generalized unique primes
|
|
|
FORMULA
|
a(n) = A085398(6^(n+1)). - Jinyuan Wang, Jan 01 2023
|
|
|
EXAMPLE
|
When k = 88, k^72 - k^36 + 1 is prime. Since this isn't prime for k < 88, a(2) = 88.
|
|
|
PROG
|
(PARI) a(n)=k=1; while(!ispseudoprime(k^(6^n)*(k^(6^n)-1)+1), k++); k
n=0; while(n<100, print1(a(n), ", "); n++)
|
|
|
CROSSREFS
|
Cf. A056993, A085398, A101406, A153436, A153438, A205506, A246119, A246120.
Sequence in context: A153228 A041401 A103013 * A356798 A356788 A224934
Adjacent sequences: A246118 A246119 A246120 * A246122 A246123 A246124
|
|
|
KEYWORD
|
nonn,more,hard,changed
|
|
|
AUTHOR
|
Serge Batalov, Aug 14 2014
|
|
|
EXTENSIONS
|
a(6) from Serge Batalov, Aug 15 2014
|
|
|
STATUS
|
approved
|
| |
|
|
