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A233591 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^2. 10
1, 2, 2, 6, 2, 8, 4, 0, 2, 4, 1, 8, 2, 6, 9, 0, 2, 7, 4, 8, 1, 4, 9, 3, 7, 1, 0, 0, 8, 6, 2, 2, 4, 0, 3, 9, 6, 1, 9, 0, 8, 1, 1, 4, 8, 7, 3, 5, 3, 6, 2, 3, 5, 9, 5, 5, 0, 1, 6, 6, 6, 5, 2, 2, 1, 2, 5, 2, 7, 5, 4, 3 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

For more details on this type of continued fractions, see A233588.

This one corresponds to the squares of natural numbers.

LINKS

Stanislav Sykora, Table of n, a(n) for n = 1..20000

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

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

FORMULA

Equals 1+1/(4+4/(9+9/(16+16/(25+25/(36+...))))).

EXAMPLE

1.22628402418269027481493710086224039619081148735362359550166652...

MATHEMATICA

RealDigits[ Fold[(#2 + #2/#1) &, 1, Reverse@ Range[45]^2], 10, 111][[1]] (* Robert G. Wilson v, May 22 2014 *)

PROG

(PARI) See the link

CROSSREFS

Cf. A000290 (n^2).

Cf. Blazys' continued fractions: A233588, A233589, A233591 and Blazys' expansions: A233582, A233583, A233584, A233585, A233586, A233587.

Sequence in context: A165460 A242649 A028330 * A071052 A193388 A208448

Adjacent sequences:  A233588 A233589 A233590 * A233592 A233593 A233594

KEYWORD

cons,nonn

AUTHOR

Stanislav Sykora, Jan 06 2014

STATUS

approved

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Last modified April 30 12:40 EDT 2017. Contains 285669 sequences.