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A245257
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Decimal expansion of y_3, the third of four non-explicit constants recursively derived from Khintchine's [Khinchin's] constant.
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3
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2, 2, 2, 4, 7, 5, 1, 4, 8, 0, 9, 8, 0, 5, 8, 3, 0, 1, 5, 3, 7, 5, 5, 9, 8, 9, 2, 4, 9, 2, 4, 1, 9, 0, 4, 2, 4, 2, 3, 6, 3, 6, 6, 7, 0, 7, 9, 8, 2, 4, 6, 6, 7, 0, 1, 6, 9, 4, 5, 6, 3, 3, 1, 5, 7, 4, 7, 1, 2, 9, 8, 7, 8, 6, 6, 2, 2, 6, 2, 4, 2, 7, 8, 4, 6, 6, 8, 4, 0, 5, 6, 6, 1, 6, 4, 9, 4, 6, 2, 3, 5, 9, 2, 4, 6
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OFFSET
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1,1
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REFERENCES
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Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 1.8.1 Alternative representations [of real numbers], p. 63.
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LINKS
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EXAMPLE
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2.224751480980583015375598924924190424236366707982466701694563315747...
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MATHEMATICA
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K = Khinchin; a[0] = pi[0] = 2; pi[n_] := Product[a[i], {i, 0, n}]; Clear[a]; a[n_?EvenQ] := a[n] = Floor[K^(n+1)/pi[n-1]]; a[n_?OddQ] := a[n] = Ceiling[K^(n+1)/pi[n-1]]; FromContinuedFraction[Array[a, 300, 0]] // RealDigits[#, 10, 105]& // First
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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