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A133618 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 8^A(k) == A(k) (mod 10^k). 17
6, 5, 8, 5, 2, 2, 5, 9, 8, 6, 1, 4, 5, 3, 0, 7, 7, 5, 1, 2, 5, 1, 8, 0, 0, 1, 5, 8, 8, 5, 5, 9, 0, 2, 6, 1, 3, 9, 1, 1, 5, 6, 2, 9, 8, 3, 7, 7, 2, 0, 1, 5, 7, 3, 8, 8, 2, 6, 6, 7, 0, 3, 7, 5, 7, 2, 7, 4, 2, 4, 4, 2, 4, 3, 7, 5, 8, 4, 4, 2, 2, 1, 3, 0, 8, 8, 8, 8, 7, 1, 5, 9, 1, 2, 0, 1, 6, 0, 9, 8, 0, 5, 3, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
COMMENTS
10-adic expansion of the iterated exponential 8^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 8^^n == 5225856 (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
658522598614530775125180015885590261391156298377201573882667037572742442437584...
8^56 == 56 (mod 100), 8^856 == 856 (mod 1000), ...
MATHEMATICA
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[8, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
CROSSREFS
Sequence in context: A298172 A225113 A329247 * A194599 A253300 A339253
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 April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)