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

Author

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

Keywords

• nonn
• base

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).

Examples

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

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, A133616, 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[7, 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