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A010123
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Continued fraction for sqrt(14).
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5
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3, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6, 1, 2, 1, 6
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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REFERENCES
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Roger Penrose, "The Road to Reality, A complete guide to the Laws of the Universe", Jonathan Cape, London, 2004, page 56. [From Olivier Gérard, May 22 2009]
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LINKS
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FORMULA
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a(n) = 1 + floor((n+2)/4) - floor((n+1)/4) + 5*(floor((n+4)/4) - floor((n+3)/4)) for n > 0. - Wesley Ivan Hurt, Apr 10 2017
Multiplicative with a(2) = 2, a(2^e) = 6 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 1/2^(2*s-2)). (End)
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EXAMPLE
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3.741657386773941385583748732... = 3 + 1/(1 + 1/(2 + 1/(1 + 1/(6 + ...)))). - Harry J. Smith, Jun 02 2009
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MATHEMATICA
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 15000); x=contfrac(sqrt(14)); for (n=0, 20000, write("b010123.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 02 2009
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CROSSREFS
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KEYWORD
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nonn,cofr,easy,mult
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AUTHOR
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STATUS
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approved
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