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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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

Examples

			0.076923076923076923076923076923076923076923...
		

References

• Florian Cajori, A History of Mathematical Notations, Dover edition (2012), par. 309.
• Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1). Princeton, New Jersey: Princeton University Press (1988): 143.

Links

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

Crossrefs

Cf. A219705.

Programs

Mathematica

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

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