A002951 Continued fraction for fifth root of 5.
1, 2, 1, 1, 1, 2, 1, 2, 8, 1, 25, 1, 5, 1, 22, 1, 8, 1, 1, 9, 1, 1, 4, 1, 2, 1, 2, 1, 2, 2, 1, 1, 1, 1, 2, 1, 6, 2, 46, 1, 12, 1, 32, 1, 2, 3, 2, 3, 55, 1, 12, 3, 8, 1, 1, 11, 1, 4, 1, 1, 1, 2, 1, 1, 7, 1, 1, 4, 3, 3, 3218, 1, 3, 1, 2, 2, 3, 1, 1, 2, 11, 1, 7, 57, 2, 2, 2, 2, 1, 1, 67, 1, 2, 3, 1, 1, 13, 3
Offset: 0
Examples
1.379729661461214832390063464... = 1 + 1/(2 + 1/(1 + 1/(1 + 1/(1 + ...)))). - _Harry J. Smith_, May 10 2009
References
- H. P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
- N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
Links
- Harry J. Smith, Table of n, a(n) for n = 0..19999
- Herman P. Robinson, Letter to N. J. A. Sloane, Nov 13 1973.
- J. Shallit & N. J. A. Sloane, Correspondence 1974-1975
- G. Xiao, Contfrac
- Index entries for continued fractions for constants
Programs
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Magma
SetDefaultRealField(RealField(100)); ContinuedFraction(5^(1/5)); // G. C. Greubel, Nov 02 2018
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Maple
with(numtheory): cfrac(5^(1/5),100,'quotients'); # Muniru A Asiru, Nov 02 2018
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Mathematica
ContinuedFraction[5^(1/5), 100] (* G. C. Greubel, Nov 02 2018 *)
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PARI
{ allocatemem(932245000); default(realprecision, 21000); x=contfrac(5^(1/5)); for (n=1, 20000, write("b002951.txt", n-1, " ", x[n])); } \\ Harry J. Smith, May 10 2009
Extensions
More terms copied from Smith's b-file by Hagen von Eitzen, Jul 20 2009
Offset changed by Andrew Howroyd, Jul 05 2024
Comments