A144543 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 15^A(k) == A(k) mod 10^k.
5, 7, 3, 9, 5, 8, 0, 8, 3, 5, 6, 7, 0, 9, 6, 0, 8, 6, 4, 4, 9, 3, 4, 6, 1, 1, 9, 2, 8, 3, 7, 9, 3, 8, 6, 2, 4, 7, 7, 8, 5, 8, 6, 5, 4, 4, 7, 2, 3, 9, 3, 0, 4, 9, 4, 3, 1, 4, 4, 1, 9, 0, 4, 9, 3, 0, 0, 1, 2, 2, 1, 9, 8, 5, 2, 4, 5, 2, 4, 5, 3, 6, 5, 5, 8, 6, 7, 2, 7, 5, 4, 7, 7, 4, 6, 9, 1, 8, 3, 8, 3, 7, 1, 5, 0
Offset: 0
Examples
573958083567096086449346119283793862477858654472393049431441904930012219852452...
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
Crossrefs
Programs
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Mathematica
(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[15, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)
Extensions
a(68) onward from Robert G. Wilson v, Mar 06 2014