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%I #22 Nov 25 2021 08:58:12
%S 0,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,
%T 6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,
%U 8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8,4,6,1,5,3,8
%N Decimal expansion of 1/26.
%C A tool code breakers sometimes use is the index of coincidence, I_c. According to Swenson (2008), the theoretically perfect I_c is if all characters occur exactly the same number of times, so that none is more likely than any other to be repeated. For cypher text encrypted from English text (using an alphabet of 26 letters) of infinite length, this has the limit (n - 1)/(26n - 1), which by L'Hopital's rule is 1/26. - _Alonso del Arte_, Sep 13 2011
%C Also continued fraction expansion of (sqrt(5317635) - 2067)/746. - _Bruno Berselli_, Sep 13 2011
%D Christopher Swenson, Modern Cryptanalysis: Techniques for Advanced Code Breaking. Indianopolis, Indiana: Wiley Publishing Inc. (2008): 12 - 15
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,-1,1).
%F Contribution by _Bruno Berselli_, Sep 13 2011: (Start)
%F G.f.: x*(3+5*x-4*x^2+5*x^3)/((1-x)*(1+x)*(1-x+x^2)).
%F a(n) = a(n-1) - a(n-3) + a(n-4) for n > 4.
%F a(n) = (1/30)*(-11*(n mod 6)+34*((n+1) mod 6) - ((n+2) mod 6) + 29*((n+3) mod 6) - 16*((n+4) mod 6) + 19*((n+5) mod 6)) for n > 0. (End)
%e 0.03846153846153846153846153846...
%t Join[{0}, RealDigits[1/26, 10, 120][[1]]] (* or *) PadRight[{0}, 120, {5, 3, 8, 4, 6, 1}] (* _Harvey P. Dale_, Dec 19 2012 *)
%K nonn,cons,easy
%O 0,2
%A _N. J. A. Sloane_.
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