A206636 a(n) = 2^^(n+2) modulo 10^n, where ^^ denotes a power tower (see A133612).

6, 36, 736, 8736, 48736, 948736, 2948736, 32948736, 432948736, 3432948736, 53432948736, 353432948736, 5353432948736, 75353432948736, 75353432948736, 5075353432948736, 15075353432948736, 615075353432948736, 8615075353432948736, 98615075353432948736, 98615075353432948736, 8098615075353432948736

Offset

1,1

Comments

Backward concatenation of A133612.

For all m>n+1, 2^^m == 2^^(n+2) (mod 10^n). Hence, each term represents the trailing decimal digits of 2^^m for every sufficiently large m.

References

Marco Ripà, La strana coda della serie n^n^...^n, Trento, UNI Service, Nov 2011. ISBN 978-88-6178-789-6.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..1000

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.

Robert G. Wilson v, Mathematica coding for "SuperPowerMod" from Vardi

Formula

a(n) = A014221(n+3) mod (10^n).

For n>1, a(n) = 2^a(n-1) mod 10^n.

Mathematica

(* first load all lines of Super Power Mod by Ilan Vardi from the hyper-link, then *) $RecursionLimit = 2^14;  a[n_] := SuperPowerMod[2, n +2, 10^n]; Array[a, 22] (* Robert G. Wilson v, Apr 20 2020 *)
(* this hard-codes the needed Chinese Remainder step using a modular inverse *) {b, M} = {2, 5}; Prepend[Rest[NestList[(M *= 5; b *= 2; b Mod[PowerMod[2, #, M] ModularInverse[b, M], M]) & , 36, 10]], 6] (* Stan Wagon, Oct 23 2025 *)

Crossrefs

Cf. A133612, A113627, A109405, A133613, A133614, A133615, A133616, A133617, A133618, A133619, A183613, A144539, A144540, A144541, A144542, A144543, A144544.

Sequence in context: A296389 A077290 A222780 * A244841 A268161 A082027

Adjacent sequences: A206633 A206634 A206635 * A206637 A206638 A206639

Keyword

nonn

Author

Marco Ripà, Feb 10 2012

Status

approved