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A133619
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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.
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3
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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
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OFFSET
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0,1
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COMMENTS
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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)
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REFERENCES
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M. Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011, p. 69-78. ISBN 978-88-6178-789-6.
J. Jimenez Urroz and J. Luis A. Yebra, On the equation a^x == x (mod b^n), Preprint, Oct 28 2008.
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LINKS
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Table of n, a(n) for n=0..67.
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CROSSREFS
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Sequence in context: A021897 A225458 A092172 * A175617 A111765 A111509
Adjacent sequences: A133616 A133617 A133618 * A133620 A133621 A133622
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KEYWORD
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nonn,base
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AUTHOR
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Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007
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EXTENSIONS
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More terms from J. Luis A. Yebra, Dec 12 2008
Edited by N. J. A. Sloane, Dec 22 2008
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STATUS
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approved
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