A021017 Decimal expansion of 1/13.

0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6, 9, 2, 3, 0, 7, 6

Offset

0,2

Comments

In 1741, Euler recognized that 10 times this number is close to (2^i + 2^(-i))/2, see Nahin (1988) and A219705. - Alonso del Arte, Nov 25 2012

Also decimal expansion of Sum_{i>=1} 1/14^i. - Bruno Berselli, Jan 03 2014

References

Florian Cajori, A History of Mathematical Notations, Dover edition (2012), par. 309.

Ross Honsberger, Ingenuity in Mathematics, Random House, 1970, p. 148.

Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1). Princeton, New Jersey: Princeton University Press (1988): 143.

Links

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

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

Formula

From Colin Barker, Aug 15 2012: (Start)

a(n) = a(n - 1) - a(n - 3) + a(n - 4).

G.f.: -x*(3*x^2 - x + 7)/((x - 1)*(x + 1)*(x^2 - x + 1)). (End)

E.g.f.: (8*cosh(x) - 4*exp(x/2)*(2*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2)) + 19*sinh(x))/3. - Stefano Spezia, Aug 05 2025

Example

0.076923076923076923076923076923076923076923...

Mathematica

LinearRecurrence[{1, 0, -1, 1}, {0, 7, 6, 9}, 98] (* with C. Barker's formula, Peter Luschny, Aug 15 2012 *)
(* Alternative: *)
Join[{0}, RealDigits[1/13, 10, 120][[1]]] (* Harvey P. Dale, Dec 17 2017 *)
(* Alternative: *)
PadRight[{}, 120, {0, 7, 6, 9, 2, 3}] (* Harvey P. Dale, Dec 17 2017 *)

Crossrefs

Cf. A219705.

Sequence in context: A351687 A011220 A198605 * A219705 A273066 A257964

Adjacent sequences: A021014 A021015 A021016 * A021018 A021019 A021020

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved