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

1,1

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

Links

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

Example

4.30323930198312254750725653712946101100587498256159332769966371810867...

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 *)

Prog

(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

Crossrefs

Sequence in context: A296002 A227423 A199443 * A296228 A267410 A016697

Adjacent sequences: A142720 A142721 A142722 * A142724 A142725 A142726

Keyword

nonn,cons

Author

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

Status

approved