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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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