A021085 Decimal expansion of 1/81.

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

Offset

0,3

Comments

The decimal expansion of Sum_{n>=1} floor(n * tanh(Pi))/10^n is the same as that of 1/81 for the first 268 decimal places [Borwein et al.]

Sqrt(999999999999999999) = 9*sqrt(12345679012345679). - Ryohei Miyadera, Ken Hirotomi, Hiroyuki Ozaki and Atushi Tanaka, Jan 16 2006

References

J. Borwein, D. Bailey and R. Girgensohn, Experimentation in Mathematics: Computational Paths to Discovery, Peters, Boston, 2004. See Sect. 1.4.

Links

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

Jean-François Alcover, 300 digits of Sum_{n>=1} floor(n*tanh(Pi))/10^n

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Formula

Equals Sum_{k >= 1} (1/2^k)*(1/5^k)*k. - Eric Desbiaux, Mar 11 2009

G.f.: x*(1 + 2*x + 3*x^2 + 4*x^3 + 5*x^4 + 6*x^5 + 7*x^6 + 9*x^7)/(1 - x^9). - Ilya Gutkovskiy, Jun 21 2016

From Stefano Spezia, Jun 03 2021: (Start)

a(n) = a(n-9) for n > 8.

Equals (1/10)*Sum_{n>0} 1/A052268(n). (End)

Mathematica

Table[Mod[n, 9], {n, 0, 120}] /. 8 -> 9 (* or *)
PadLeft[First@ #, Abs@ Last@ # + Length@ First@ #] &@ RealDigits[N[1/81, 120]] (* Michael De Vlieger, Jun 21 2016 *)
PadRight[{}, 120, {0, 1, 2, 3, 4, 5, 6, 7, 9}](* Harvey P. Dale, Apr 07 2019 *)

Crossrefs

Cf. A052268.

Sequence in context: A228052 A308072 A084689 * A031006 A031978 A304481

Adjacent sequences: A021082 A021083 A021084 * A021086 A021087 A021088

Keyword

nonn,easy,cons

Author

N. J. A. Sloane

Status

approved