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

Author

N. J. A. Sloane

Keywords

• nonn
• cons
• easy

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 ciphertext 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

Examples

			0.03846153846153846153846153846...
		

References

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

Links

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

Programs

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 *)

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)