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.

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

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 [a(322) onward corrected by Kevin Ryde, Oct 28 2024]

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 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: A028330 A293524 A363831 * A071052 A305984 A193388

Adjacent sequences: A233588 A233589 A233590 * A233592 A233593 A233594

Keyword

cons,nonn

Author

Stanislav Sykora, Jan 06 2014

Status

approved