A020793 Decimal expansion of 1/6.

1, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Except for the first term identical to A010722, A040006 and A021019. Except for the first terms the same as A021028, A021100, A021388, A071279, A101272, A168608, A177057,... - M. F. Hasler, Oct 24 2011

Decimal expansion of gamma(1) = 5/3 (with offset 1), where gamma(n) = Cp(n)/Cv(n) = is the n-th Poisson's constant. For the definition of Cp and Cv see A272002. - Natan Arie Consigli, Jul 10 2016

References

• Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Springer, 2013, see p. 224.

Links

• Wikipedia, Poisson's constant.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A010722, A021019, A021028, A021100, A021388, A040006, A070064, A071279, A081822, A101272, A168608, A177057, A272001, A272002.

Programs

Mathematica

RealDigits[1/6,10,120][[1]] (* or *) PadRight[{1},120,{6}] (* Harvey P. Dale, Dec 30 2018 *)

PARI

a(n)=6-5*!n  \\ M. F. Hasler, Oct 24 2011

Formula

a(n) = 6^n mod 10. - Zerinvary Lajos, Nov 26 2009

Equals Sum_{k>=1} 1/7^k. - Bruno Berselli, Jan 03 2014

10 * 1/6 = 5/3 = (5/2 R)/(3/2 R) = Cp(1)/Cv(1) = A272002/A272001, with R = A081822 (or A070064). - Natan Arie Consigli, Jul 10 2016

G.f.: (1 + 5*x)/(1 - x). - Ilya Gutkovskiy, Jul 10 2016

Equals Sum_{k>=1} 1/(k*Pi)^2. - Maciej Kaniewski, Sep 14 2017

Equals Sum_{k>=1} (zeta(2*k)-1)/4^k. - Amiram Eldar, Jun 08 2021

K_{n>=2} 2*n/(2*n - 3) = 5/3. (see Clawson at p. 224). - Stefano Spezia, Jul 01 2024

E.g.f.: 6*exp(x) - 5. - Elmo R. Oliveira, Aug 05 2024