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A076635
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Let b(1)=1/n, b(2)=1, b(k+1)=abs(b(k))-b(k-1)^2; then b(k) is >0 for k>a(n).
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0
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5, 8, 12, 11, 11, 15, 14, 14, 14, 18, 18, 17, 17, 17, 17, 17, 21, 20, 21, 21, 21, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 20, 24, 24, 24, 24, 25, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 23, 28, 27, 27, 27, 27, 27, 27, 27, 28, 26, 26, 26, 26, 26, 26
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OFFSET
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1,1
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COMMENTS
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Conjecture: lim k->infinity (b(k)-k)/log(k) = f(n), constant depending on n. f(n) seems erratic: f(2)=2.9..., f(3)=2.5..., f(4)=3.2..., f(5)=2.25..., f(6)=4.0...
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LINKS
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FORMULA
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a(n) seems to be asymptotic to c*log(n) with c=5.63...
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EXAMPLE
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If n=4, b(11)<0 and b(k)>0 for any k>11 hence a(4)=11.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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