A133617 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 7^A(k) == A(k) (mod 10^k).

3, 4, 3, 2, 7, 1, 5, 6, 5, 1, 1, 5, 5, 6, 2, 1, 3, 3, 3, 4, 6, 3, 5, 8, 3, 3, 3, 7, 3, 6, 0, 8, 6, 0, 3, 6, 9, 5, 6, 7, 4, 1, 8, 2, 6, 6, 5, 9, 2, 6, 5, 3, 0, 8, 6, 5, 2, 8, 4, 4, 4, 7, 7, 7, 6, 7, 5, 4, 9, 1, 2, 9, 8, 6, 5, 7, 7, 0, 7, 8, 4, 2, 6, 3, 8, 5, 4, 8, 1, 9, 4, 5, 8, 3, 9, 9, 5, 4, 4, 0, 3, 8, 2, 2, 0

Offset

0,1

Comments

10-adic expansion of the iterated exponential 7^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 7^^n == 5172343 (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

343271565115562133346358333736086036956741826659265308652844477767549129865770...
Sequences A133612-A144544 generalize the observation that 7^343 == 343 (mod 1000).

Mathematica

(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[7, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)

Crossrefs

Cf. A133612, A133613, A133614, A133615, A133616, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.

Sequence in context: A164358 A275638 A281975 * A199286 A188722 A257526

Adjacent sequences: A133614 A133615 A133616 * A133618 A133619 A133620

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