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A080984
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Define b by b(1) = 1 and for n > 1, b(n) = b(n-1) + 1/(2 + 1/b(n-1)); sequence gives numerator of b(n).
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2
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OFFSET
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1,2
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COMMENTS
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LINKS
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FORMULA
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b(k) = n(k)/d(k); n(1)=1, d(1)=1, m=2; for k >= 2: n(k+1) = n(k) *(m*n(k) + 2*d(k)), d(k+1) = d(k)*(m*n(k) + d(k)). - Leroy Quet
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EXAMPLE
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The sequence {b(n)} begins 1, 4/3, 56/33, 9968/4785, 294115808/118289985, ...
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MATHEMATICA
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Numerator/@NestList[#+1/(2+1/#)&, 1, 9] (* Harvey P. Dale, Jul 07 2011 *)
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PROG
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Reduce: a := 1; for i := 1:8 do write a := a+1/(2+1/a);
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CROSSREFS
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KEYWORD
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frac,nonn
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AUTHOR
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STATUS
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approved
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