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Search: id:A076635
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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
1
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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
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Conjecture : lim k->infinity (b(k)-k)/ln(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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FORMULA
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a(n) seems to be asymptotic to c*ln(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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Adjacent sequences: A076632 A076633 A076634 this_sequence A076636 A076637 A076638
Sequence in context: A023381 A133522 A133269 this_sequence A116602 A079896 A133315
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Oct 23 2002
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