A021030 Decimal expansion of 1/26.

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, 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, 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

Offset

0,2

Comments

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

Also continued fraction expansion of (sqrt(5317635) - 2067)/746. - Bruno Berselli, Sep 13 2011

References

Christopher Swenson, Modern Cryptanalysis: Techniques for Advanced Code Breaking. Indianopolis, Indiana: Wiley Publishing Inc. (2008): 12 - 15

Links

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

Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Formula

Contribution by Bruno Berselli, Sep 13 2011: (Start)

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

a(n) = a(n-1) - a(n-3) + a(n-4) for n > 4.

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)

Example

0.03846153846153846153846153846...

Mathematica

Join[{0}, RealDigits[1/26, 10, 120][[1]]] (* or *) PadRight[{0}, 120, {5, 3, 8, 4, 6, 1}] (* Harvey P. Dale, Dec 19 2012 *)

Crossrefs

Sequence in context: A242030 A105722 A103559 * A276682 A303215 A240242

Adjacent sequences: A021027 A021028 A021029 * A021031 A021032 A021033

Keyword

nonn,cons,easy

Author

N. J. A. Sloane.

Status

approved