A133616 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 6^A(k) == A(k) (mod 10^k).

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

Offset: 0

Author

Daniel Geisler (daniel(AT)danielgeisler.com), Dec 18 2007

Keywords

• nonn
• base

Comments

10-adic expansion of the iterated exponential 6^^n for sufficiently large n (where c^^n denotes a tower of c's of height n). E.g., for n > 9, 6^^n == 7238656 (mod 10^7).

Examples

			656832744722395569767321960175060586918013794604470464024637816708501434441857...
		

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

Cf. A133612, A133613, A133614, A133615, A133617, A133618, A133619, A144539, A144540, A144541, A144542, A144543, A144544.

Programs

Mathematica

(* Import Mmca coding for "SuperPowerMod" and "LogStar" from text file in A133612 and then *) $RecursionLimit = 2^14; f[n_] := SuperPowerMod[6, n + 1, 10^n]; Reverse@ IntegerDigits@ f@ 105 (* Robert G. Wilson v, Mar 06 2014 *)

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