The number of \(k\)-digit Fibonacci numbers (Q2746561)
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scientific article; zbMATH DE number 1656222
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The number of \(k\)-digit Fibonacci numbers |
scientific article; zbMATH DE number 1656222 |
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16 September 2002
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number of \(k\)-digit Fibonacci numbers
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0.90290797
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The number of \(k\)-digit Fibonacci numbers (English)
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Define \(a(k)\) to be the number of \(k\)-digit Fibonacci numbers. Then one has \(a(k)=4\) or \(a(k)=5\) for \(k>1\). Let \(A(x,q,\ell)\) be the number of \(k\leq x\), \(k\equiv \ell\pmod q\) such that \(a(k)=5\). Then for any fixed \(q\) it is shown that \(A(x,q,\ell)\sim \frac{\alpha}{q} x\), where \(\alpha= \log 10/\log ((1+\sqrt{5})/2)-4= 0.78497\dots\;\).
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