A142723 Decimal expansion of the continued fraction whose terms are half the gaps of the odd nonprimes A014076.

4, 3, 0, 3, 2, 3, 9, 3, 0, 1, 9, 8, 3, 1, 2, 2, 5, 4, 7, 5, 0, 7, 2, 5, 6, 5, 3, 7, 1, 2, 9, 4, 6, 1, 0, 1, 1, 0, 0, 5, 8, 7, 4, 9, 8, 2, 5, 6, 1, 5, 9, 3, 3, 2, 7, 6, 9, 9, 6, 6, 3, 7, 1, 8, 1, 0, 8, 6, 7, 0, 5, 5, 2, 1, 6, 2, 6, 3, 9, 5, 7, 8, 9, 0, 1, 9, 6, 0, 0, 2, 4, 3, 7, 4, 8, 7, 1, 5, 5, 8, 7, 3, 6, 9, 2

Offset: 1

Author

Roger L. Bagula and Gary W. Adamson, Sep 27 2008

Keywords

• nonn
• cons

Comments

Take half of the first difference of odd nonprimes A014076 and treat it as a continued fraction. This sequence gives the decimal expansion of that number. - Charles R Greathouse IV, Feb 03 2011

Examples

			4.30323930198312254750725653712946101100587498256159332769966371810867...
		

Links

• G. C. Greubel, Table of n, a(n) for n = 1..5000

Programs

Mathematica

a = Flatten[Table[If[PrimeQ[2*n + 1], {}, 2*n - 1], {n, 0, 200}]]; b = Table[(a[[n + 1]] - a[[n]])/2, {n, 1, Length[a] - 1}]; FromContinuedFraction[b]; c = N[%, 200]; Table[Floor[Mod[c*10^n, 10]], {n, 0, 201}] (* Bagula and Adamson *)
RealDigits[FromContinuedFraction[Differences[Select[Range[-1, 399, 2], !PrimeQ[# + 2]&]]/2], 10, 201][[1]] (* Charles R Greathouse IV, Feb 03 2011 *)

PARI

a=contfracpnqn(D(select(vector(99,n,2*n-1),x->!isprime(x)))/2); a[1,1]/a[2,1]*1.  /* OK for 35 digits. For D(.) see A137822 */ \\ M. F. Hasler, Sep 29 2011