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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. 16
 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. RipĂ , 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 Robert G. Wilson v, Table of n, a(n) for n = 0..1024 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 Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133619, A144539, A144540, A144541, A144542, A144543, A144544. Sequence in context: A021607 A298172 A225113 * A194599 A253300 A080799 Adjacent sequences:  A133615 A133616 A133617 * A133619 A133620 A133621 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 May 25 19:58 EDT 2019. Contains 323576 sequences. (Running on oeis4.)