A144539 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 11^A(k) == A(k) mod 10^k.

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

Offset: 0

Author

N. J. A. Sloane, Dec 20 2008

Keywords

• nonn
• base

Examples

			116666271978307662027198793432698117510204594399945393924384160568806429261664...
		

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, A133617, A133618, A133619, 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[11, 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