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

Author

Stanislav Sykora, Jan 06 2014

Keywords

• cons
• nonn

Comments

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

This one corresponds to the squares of natural numbers.

Examples

			1.22628402418269027481493710086224039619081148735362359550166652...
		

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

Crossrefs

Cf. A000290 (n^2).

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

Programs

Mathematica

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

PARI

See the link

Formula

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