Thread Rating:
  • 0 Vote(s) - 0 Average
  • 1
  • 2
  • 3
  • 4
  • 5
Integer tetration and convergence speed rules
#6
We can also construct some bases with an unlimited convergence speed, for example, 999...9. The number of "9" (the lenght in digits of the base) gives us an equal "convergence speed in a single step": i.e. [9999999^^n](mod 10^(7*n))==[9999999^^(n+1)](mod 10^(7*n)).

Marco
Let G(n) be a generic reverse-concatenated sequence. If G(1)≠{2, 3, 7}, [G(n)^^G(n)](mod 10^d)≡[G(n+1)^^G(n+1)](mod 10^d), ∀n∈N\{0} (La strana coda della serie n^n^...^n, 60).
Reply


Messages In This Thread
RE: Integer tetration and convergence speed rules - by marcokrt - 12/21/2011, 06:21 PM

Possibly Related Threads...
Thread Author Replies Views Last Post
  Thoughts on hyper-operations of rational but non-integer orders? VSO 2 778 09/09/2019, 10:38 PM
Last Post: tommy1729
  Where is the proof of a generalized integral for integer heights? Chenjesu 2 1,196 03/03/2019, 08:55 AM
Last Post: Chenjesu
  Isomorphism of newtonian calculus rules for Non-Newtonian (anti)derivatives of hypers Micah 4 1,672 03/02/2019, 08:23 PM
Last Post: Micah
  Tetration series for integer exponent. Can you find the pattern? marraco 20 17,876 02/21/2016, 03:27 PM
Last Post: marraco
  Lit: f(x)=log(x) iff x is integer Gottfried 3 4,968 03/17/2015, 11:35 PM
Last Post: tommy1729
  Tommy's conjecture : every positive integer is the sum of at most 8 pentatope numbers tommy1729 0 2,233 08/17/2014, 09:01 PM
Last Post: tommy1729
  What is the convergence radius of this power series? JmsNxn 9 16,416 07/04/2011, 09:08 PM
Last Post: JmsNxn
  2 [n] b and 3 [n] b for (large) integer n, b dyitto 2 3,946 03/12/2011, 10:52 PM
Last Post: dyitto
  Nowhere analytic superexponential convergence sheldonison 14 18,946 02/10/2011, 07:22 AM
Last Post: sheldonison
  using the sum , hoping for convergence tommy1729 4 5,550 08/28/2010, 12:10 PM
Last Post: tommy1729



Users browsing this thread: 1 Guest(s)