A066746 Conjectured values of a(n) defined by a(n) = least number of applications of f(k) = k^2 + 1 to n to yield a prime, if this number exists; = -1 otherwise.

1, 0, 0, 1, 0, 1, 0, 3, -1, 1, 0

Offset

1,8

Comments

a(9) = -1 is conjectural. If a(9) is positive, then a(9) > 14. (f^15)(9) already has several thousand digits. (f^n denotes f applied n times.)

From James Rayman, Jan 18 2021: (Start)

If a(9) is positive, then a(9) > 53. For all 0 <= n <= 53, (f^n)(9) has a prime factor less than 10^9. (f^54)(9) has no prime factors less than 2*10^10.

If a(9) is positive, (f^a(9))(9) would be a prime with at least 10^16 digits. In comparison, the largest known prime at the time of writing has about 2*10^7 digits. (End)

Links

Table of n, a(n) for n=1..11.

Example

f(f(f(8))) = f(f(65)) = f(4226) = 17859077, a prime. Since 8, 65, 4226 are composite, then a(8) = 3.

Crossrefs

Sequence in context: A327547 A233293 A361579 * A278105 A074063 A338211

Adjacent sequences: A066743 A066744 A066745 * A066747 A066748 A066749

Keyword

more,sign

Author

Joseph L. Pe, Jan 16 2002

Status

approved