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%I #24 Dec 17 2017 13:35:16
%S 0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,
%T 2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,
%U 6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6,9,2,3,0,7,6
%N Decimal expansion of 1/13.
%C In 1741, Euler recognized that 10 times this number is close to (2^i + 2^(-i))/2, see Nahin (1988) and A219705. - _Alonso del Arte_, Nov 25 2012
%C Also decimal expansion of sum(i=1..infinity, 1/14^i). [_Bruno Berselli_, Jan 03 2014]
%D Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1). Princeton, New Jersey: Princeton University Press (1988): 143.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1).
%F a(n) = a(n - 1) - a(n - 3) + a(n - 4). G.f.: -x*(3*x^2 - x + 7)/((x - 1)*(x + 1)*(x^2 - x + 1)). [_Colin Barker_, Aug 15 2012]
%e 0.076923076923076923076923076923076923076923...
%t LinearRecurrence[{1, 0, -1, 1}, {0, 7, 6, 9}, 98] (* with C. Barker's formula, _Peter Luschny_, Aug 15 2012 *)
%t Join[{0},RealDigits[1/13,10,120][[1]]] (* or *) PadRight[{},120,{0,7,6,9,2,3}] (* _Harvey P. Dale_, Dec 17 2017 *)
%Y Cf. A219705.
%K nonn,cons,easy
%O 0,2
%A _N. J. A. Sloane_.
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