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)

EXAMPLE

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

CROSSREFS

KEYWORD

more,sign

AUTHOR

Joseph L. Pe, Jan 16 2002

STATUS

approved