A133619 - OEIS

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).

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

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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

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

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.

Cf. A133612, A133613, A133614, A133615, A133616, A133617, A133618, A144539, A144540, A144541, A144542, A144543, A144544.

Sequence in context: A021897 A225458 A092172 * A276499 A175617 A111765

Adjacent sequences: A133616 A133617 A133618 * A133620 A133621 A133622

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