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A246121 Least k such that k^(6^n)*(k^(6^n)-1)+1 is prime. 3
2, 3, 88, 28, 688, 7003, 1925 (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=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

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. A205506, A246119, A246120, A153438, A101406, A153436, A056993.

Sequence in context: A153228 A041401 A103013 * A224934 A299691 A042901

Adjacent sequences:  A246118 A246119 A246120 * A246122 A246123 A246124

KEYWORD

nonn,more,hard

AUTHOR

Serge Batalov, Aug 14 2014

EXTENSIONS

a(6) from Serge Batalov, Aug 15 2014

STATUS

approved

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