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A040052
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Continued fraction for sqrt(60).
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4
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7, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14, 1, 2, 1, 14
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graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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FORMULA
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G.f.: (7 + x + 2*x^2 + x^3 + 7*x^4)/(1-x^4).
a(n) = (6*(-i)^n + 6*i^n + 7*(-1)^n + 9)/2 - 7*A000007(n), where i is the imaginary unit. (End)
Multiplicative with a(2) = 2, a(2^e) = 14 for e >= 2, and a(p^e) = 1 for an odd prime p.
Dirichlet g.f.: zeta(s) * (1 + 1/2^s + 3/4^(s-1)). (End)
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EXAMPLE
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7.74596669241483377035853079... = 7 + 1/(1 + 1/(2 + 1/(1 + 1/(14 + ...)))). - Harry J. Smith, Jun 07 2009
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MAPLE
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Digits := 100: convert(evalf(sqrt(N)), confrac, 90, 'cvgts'):
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MATHEMATICA
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PROG
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(PARI) { allocatemem(932245000); default(realprecision, 19000); x=contfrac(sqrt(60)); for (n=0, 20000, write("b040052.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 07 2009
(Magma) [7] cat &cat[ [1, 2, 1, 14]: n in [1..18]]; // Bruno Berselli, Mar 07 2011
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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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