A133614 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 4^A(k) == A(k) (mod 10^k).

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

Offset

0,1

Comments

10-adic expansion of the iterated exponential 4^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 4^^n == 1728896 (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

698827114092555203226394953143931206575634213526062954066075956906146883836488...

Mathematica

(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[4, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)

Crossrefs

Cf. A133612, A133613, A133615, A133616, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.

Sequence in context: A340808 A233589 A199282 * A255674 A019753 A200105

Adjacent sequences: A133611 A133612 A133613 * A133615 A133616 A133617

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