

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
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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: A293514 A028330 A293524 * A071052 A305984 A193388
Adjacent sequences: A233588 A233589 A233590 * A233592 A233593 A233594


KEYWORD

cons,nonn


AUTHOR

Stanislav Sykora, Jan 06 2014


STATUS

approved



