A177057 - OEIS

%I #16 Oct 05 2024 22:14:23

%S 1,1,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,

%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 6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6

%N Decimal expansion of 7/6.

%C 7/6 is the 14th Bernoulli number. - _Jean-François Alcover_, Dec 24 2013

%H Michael I. Shamos, <a href="http://euro.ecom.cmu.edu/people/faculty/mshamos/cat.pdf">A catalog of the real numbers</a>, (2007). See pp. 208-209.

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

%F From _Elmo R. Oliveira_, Aug 03 2024: (Start)

%F G.f.: x*(1 + x) + 6*x^3/(1 - x).

%F E.g.f.: 6*exp(x) - 5*(1 + x).

%F a(n) = 6, n >= 3. (End)

%F Equals zeta(4)^2/zeta(8) = Sum_{k>=1} 2^omega(k)/k^4 = Product_{p prime} (p^4 + 1)/(p^4 - 1). See Shamos link. - _Stefano Spezia_, Oct 05 2024

%e 1.16666666666...

%t RealDigits[7/6,10,120][[1]] (* or *) PadRight[{1,1},120,{6}] (* _Harvey P. Dale_, Nov 20 2023 *)

%Y Cf. A177022, A177056.

%K nonn,cons,easy

%O 1,3

%A _Vincenzo Librandi_, May 26 2010

%E Edited by _Rick L. Shepherd_, Jun 17 2010