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

0,2

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

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

H. F. Sandham, Three summations due to Ramanujan, The Quarterly Journal of Mathematics, Vol. 1, No. 1 (1950), pp. 238-240.

H. F. Sandham, Some infinite series, Proc. Amer. Math. Soc., Vol. 5 (1954), pp. 430-436. See p. 430, eq. 1.41.

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

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)

Equals Sum_{k>=1} (-1)^(k+1)*k/(exp(k*Pi) + (-1)^k). - Amiram Eldar, Apr 08 2026

Example

0.04166666666666666666666666666666666666666666666666...

Mathematica

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

Crossrefs

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

Sequence in context: A008565 A205325 A021100 * A193529 A214561 A066575

Adjacent sequences: A021025 A021026 A021027 * A021029 A021030 A021031

Keyword

nonn,cons,easy

Author

N. J. A. Sloane

Status

approved