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A133619 Unique sequence of digits a(0), a(1), a(2), ... such that for all k >= 2, the number A(k) := Sum_{n = 0..k-1} a(n)*10^n satisfies 9^A(k) == A(k) (mod 10^k). 17
9, 8, 2, 5, 4, 7, 2, 9, 3, 7, 9, 5, 7, 8, 0, 8, 4, 7, 0, 1, 6, 5, 7, 4, 3, 0, 5, 6, 2, 7, 2, 8, 4, 5, 2, 5, 7, 0, 0, 5, 8, 9, 9, 8, 8, 7, 4, 0, 4, 1, 9, 4, 9, 8, 8, 6, 8, 4, 6, 8, 1, 9, 9, 2, 6, 2, 0, 1, 3, 7, 5, 4, 1, 6, 1, 3, 6, 0, 7, 3, 8, 5, 8, 4, 6, 0, 0, 2, 0, 6, 3, 2, 5, 3, 7, 6, 7, 2, 9, 5, 7, 4, 3, 2, 4 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 9^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 9^^n == 2745289 (mod 10^7).
REFERENCES
M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
Ilan Vardi, "Computational Recreations in Mathematica," Addison-Wesley Publishing Co., Redwood City, CA, 1991, pages 226-229.
LINKS
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), J. Int. Seq. 12 (2009) #09.8.8.
EXAMPLE
982547293795780847016574305627284525700589988740419498868468199262013754161360...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[9, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Cf. A306686.
Sequence in context: A021897 A225458 A092172 * A276499 A175617 A111765
KEYWORD
nonn,base
AUTHOR
Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
EXTENSIONS
More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
a(68) onward from Robert G. Wilson v, Mar 06 2014
STATUS
approved

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Last modified July 20 17:48 EDT 2024. Contains 374459 sequences. (Running on oeis4.)