A216099 Period of powers of 3 mod 10^n.

4, 20, 100, 500, 5000, 50000, 500000, 5000000, 50000000, 500000000, 5000000000, 50000000000, 500000000000, 5000000000000, 50000000000000, 500000000000000, 5000000000000000, 50000000000000000, 500000000000000000, 5000000000000000000, 50000000000000000000, 500000000000000000000

Offset

1,1

Links

Table of n, a(n) for n=1..22.

Index entries for linear recurrences with constant coefficients, signature (10).

Formula

a(n) = 4*5^(n-1) for n <= 4.

a(n) = 5*10^(n-2) for n >= 5.

From Elmo R. Oliveira, Apr 02 2026: (Start)

a(n) = A216164(n+1).

a(n) = 10*a(n-1) for n > 4.

G.f.: 4*x*(125*x^3 + 25*x^2 + 5*x - 1)/(10*x - 1).

E.g.f.: (1/60)*(3*exp(10*x) - 3 + 210*x + 450*x^2 + 500*x^3). (End)

Mathematica

Table[If[n<5, (4*5^n)/5, 10^n/20], {n, 20}] (* or *) Join[{4, 20, 100}, NestList[ 10#&, 500, 20]] (* Harvey P. Dale, May 31 2017 *)

Prog

(PARI) a(n)=if(n<5, 4*5^n/5, 10^n/20) \\ Charles R Greathouse IV, Mar 26 2016

Crossrefs

Cf. A000244, A001148, A001218, A093143, A216164.

Sequence in context: A103771 A005054 A370536 * A395583 A105480 A242156

Adjacent sequences: A216096 A216097 A216098 * A216100 A216101 A216102

Keyword

nonn,base,easy

Author

V. Raman, Sep 01 2012

Status

approved