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A010146
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Continued fraction for sqrt(62).
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4
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7, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14, 1, 6, 1, 14
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| Eventually periodic with period 4.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=0,...,20000
G. Xiao, Contfrac
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1).
Index entries for continued fractions for constants
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FORMULA
| a(n)=(1/6)*{-14*(n mod 4)+13*[(n+1) mod 4]-2*[(n+2) mod 4]+25*[(n+3) mod 4]}-7*[C(2*n,n) mod 2], with n>=0 [From Paolo P. Lava (paoloplava(AT)gmail.com), Jul 24 2009]
a(n) = 1+(1+(-1)^n)*(9+4*i^n)/2 - 7*A000007(n), where i is the imaginary unit. - Bruno Berselli, Mar 08 2011 - Mar 15 2011
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EXAMPLE
| 7.87400787401181101968503444... = 7 + 1/(1 + 1/(6 + 1/(1 + 1/(14 + ...)))) [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 07 2009]
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MATHEMATICA
| ContinuedFraction[Sqrt[62], 300] (*From Vladimir Joseph Stephan Orlovsky, Mar 08 2011*)
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PROG
| (PARI) { allocatemem(932245000); default(realprecision, 22000); x=contfrac(sqrt(62)); for (n=0, 20000, write("b010146.txt", n, " ", x[n+1])); } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 07 2009]
(MAGMA) [7] cat &cat[ [1, 6, 1, 14]: n in [1..18]]; // Bruno Berselli, Mar 08 2011
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CROSSREFS
| Cf. A010515 Decimal expansion. [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jun 07 2009]
Sequence in context: A107786 A154932 A026497 * A176438 A092615 A199279
Adjacent sequences: A010143 A010144 A010145 * A010147 A010148 A010149
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KEYWORD
| nonn,cofr,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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