A021028 Decimal expansion of 1/24.

0, 4, 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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

Comments

Divided by 10, this is zeta(-7), where zeta is the Riemann zeta function. - Alonso del Arte, Jan 13 2012

References

• L. B. W. Jolley, Summation of series, Dover Publications Inc. (New York), 1961, p. 40 (series n. 210).

Links

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

Crossrefs

Cf. A016777 (numbers of the form 3n+1).

Programs

Mathematica

RealDigits[1/24, 10, 100, -1][[1]] (* Alonso del Arte, Jan 13 2012 *)

Formula

Equals 1/(1*4*7) + 1/(4*7*10) + 1/(7*10*13) + 1/(10*13*16) + ... = Sum_{i>=0} 1/((3i+1)*(3i+4)*(3i+7)). - Bruno Berselli, Mar 21 2014

Equals Sum_{k >= 1} k^13/(e^(2*k*Pi) - 1) (by Ramanujan). - Paolo Xausa, Jul 15 2024

From Stefano Spezia, Aug 06 2024: (Start)

G.f.: x*(4 - 3*x + 5*x^2)/(1 - x).

E.g.f.: 6*(exp(x) - 1) - 2*x - 5*x^2/2. (End)