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A192543
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Let r be the largest real zero of x^n - x^(n-1) - x^(n-2) - ... - 1 = 0. Then a(n) is the value of k which satisfies the equation 0.5/10^k < 2 - r < 5/10^k.
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1
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0, 1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 21, 21, 21, 22, 22, 22
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OFFSET
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1,5
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COMMENTS
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LINKS
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EXAMPLE
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For n = 5, the root is approximately r = 1.96594823. The value of k that satisfies 0.5/10^k < 2-r < 5/10^k is 2 as 0.005 < 0.03405177 < 0.05. So a(5) = 2.
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PROG
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(PARI) a(n)=if(n>1, -log(4-2*solve(x=1.5, 2, x^n-(1-x^n)/(1-x)))\log(10)+1, 0) \\ Charles R Greathouse IV, Jan 15 2013
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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