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Decimal expansion of 1/24.
6

%I #33 Aug 06 2024 14:52:02

%S 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,

%T 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%U 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Decimal expansion of 1/24.

%C Divided by 10, this is zeta(-7), where zeta is the Riemann zeta function. - _Alonso del Arte_, Jan 13 2012

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

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F 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

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

%F From _Stefano Spezia_, Aug 06 2024: (Start)

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

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

%t RealDigits[1/24, 10, 100, -1][[1]] (* _Alonso del Arte_, Jan 13 2012 *)

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

%K nonn,cons,easy

%O 0,2

%A _N. J. A. Sloane_