A233589 Decimal expansion of the continued fraction c(1) +c(1)/(c(2) +c(2)/(c(3) +c(3)/(c(4) +c(4)/....))), where c(i)=(i-1)!.

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

Offset

1,2

Links

Stanislav Sykora, Table of n, a(n) for n = 1..20000 (terms 6942..20000 corrected by Amiram Eldar)

Stanislav Sykora, Blazys' Expansions and Continued Fractions, Stans Library, Vol.IV, 2013, DOI 10.3247/sl4math13.001

Stanislav Sykora, PARI/GP scripts for Blazys expansions and fractions, OEIS Wiki.

Formula

Equals 0!+0!/(1!+1!/(2!+2!/(3!+3!/(4!+...)))).

Equals simple continued fraction [0!!; 1!!, 2!!, 3!!, ..., n!!, ...] where the double factorial n!! = A006882(n). - Thomas Ordowski, Oct 21 2024

Example

1.69880476767000721195269011591464043255973093664983969781741917426892...

Mathematica

RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ Range[0, 18]!], 10, 111][[1]] (* Robert G. Wilson v, May 22 2014 *)

Prog

(PARI) See the link.

Crossrefs

Cf. A233588.

Cf. A000142 (factorials), A006882 (double factorials).

Cf. Blazys' continued fractions: A233588, A233590, A233591 and Blazys' expansions: A233582, A233583, A233584, A233585, A233586, A233587.

Sequence in context: A198214 A374643 A340808 * A199282 A133614 A255674

Adjacent sequences: A233586 A233587 A233588 * A233590 A233591 A233592

Keyword

cons,nonn

Author

Stanislav Sykora, Jan 06 2014

Status

approved