A021105 Decimal expansion of 1/101.

0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9, 9, 0, 0, 9

Offset

0,3

Links

Table of n, a(n) for n=0..98.

Index entries for linear recurrences with constant coefficients, signature (1,-1,1).

Formula

From Wesley Ivan Hurt, Jun 04 2016: (Start)

G.f.: 9*x^2/(1-x)*(1+x^2).

a(n) = a(n-1) - a(n-2) + a(n-3) for n>2.

a(n) = 9*(1+(-1)^((2*n+3+(-1)^n)/4))/2 = 9*A133872(n+2).

a(n) = 9*(1+i)*(1-i-i^(-n)+i^(1+n))/4 where i=sqrt(-1).

a(2k) = A010680(k), a(2k+1) = A010680(k+1). (End)

E.g.f.: 9*(-sin(x) - cos(x) + sinh(x) + cosh(x))/2. - Ilya Gutkovskiy, Jun 04 2016

Maple

Digits:=100: evalf(1/101); # Wesley Ivan Hurt, Jun 04 2016

Mathematica

Flatten[RealDigits[1/101, 10, 100, -1]] (* Wesley Ivan Hurt, Jun 04 2016 *)

Prog

(PARI) a(n) = {r=lift(Mod(10, 101)^(n-1)); floor(10*r/101)} \\ Michael B. Porter, Oct 01 2009

Crossrefs

Cf. A010680, A133872.

Sequence in context: A180680 A165398 A329716 * A334711 A176537 A019891

Adjacent sequences: A021102 A021103 A021104 * A021106 A021107 A021108

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved