A010722 Constant sequence: the all 6's sequence.

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
• easy

Comments

Continued fraction expansion of 3+sqrt(10). - Bruno Berselli, Mar 15 2011

Decimal expansion of Sum_{n >= 0} n/binomial(2*n+1, n) = 2/3. - Bruno Berselli, Sep 14 2015

Decimal expansion of 2/3. - Franklin T. Adams-Watters, Feb 23 2019

References

• John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See p. 81.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987, p. 29.

Links

• INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 1014.
• Tanya Khovanova, Recursive Sequences.
• Index to divisibility sequences.
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

Cf. A145429: decimal expansion of Sum_{n >= 0} n/binomial(2*n, n).

Cf. A000012, A007395, A010701, A010709, A010716.

First differences of A008588.

Programs

PARI

a(n)=6 \\ Charles R Greathouse IV, Sep 28 2015

Formula

G.f.: 6/(1-x). - Bruno Berselli, Mar 15 2011

E.g.f.: 6*e^x. - Vincenzo Librandi, Jan 27 2012

a(n) = floor(1/(-n + csc(1/n))). - Clark Kimberling, Mar 10 2020