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Search: id:A065560
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| A065560 |
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Let f(x,y) = floor((1+1/x)^y); a(n) is the smallest integer such that f(n,a(n)+1)/f(n,a(n)) = 1+1/n. |
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4
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| 2, 4, 7, 9, 12, 15, 18, 21, 25, 28, 40, 35, 39, 42, 46, 50, 54, 58, 62, 66, 70, 74, 78, 83, 87, 91, 95, 100, 104, 109, 113, 118, 122, 127, 131, 136, 141, 145, 150, 155, 159, 164, 169, 174, 179, 183, 188, 193, 198, 203, 208
(list; graph; listen)
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OFFSET
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2,1
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COMMENT
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a(n) is growing roughly like prime(n). a(n) < a(n+1) except for n = 12 (only?)...
a(n) < a(n+1) except for n = 12, 108, 266, ... - Boris Gourevitch (boris(AT)pi314.net), Dec 04 2001
Conjecture : a(n)+n > prime(n)
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FORMULA
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Asymptotic (conjectured) formula: a(n)=n*ln(n)+o(ln(n))
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EXAMPLE
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a(5) = 9 because 9 is the first integer satisfying floor((6/5)^(9+1))/floor((6/5)^9) = 6/5.
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CROSSREFS
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Cf. A065554, A065564.
Adjacent sequences: A065557 A065558 A065559 this_sequence A065561 A065562 A065563
Sequence in context: A065027 A026356 A031435 this_sequence A134886 A024193 A064550
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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), Nov 29 2001
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