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A097051
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a(n) = floor(n/a(floor(n/2))); a(1) = 1.
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3
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1, 2, 3, 2, 2, 2, 2, 4, 4, 5, 5, 6, 6, 7, 7, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8
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OFFSET
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1,2
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LINKS
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FORMULA
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If floor(log_2(n))=2k+1, then a(n) = floor(n/2^k). If floor(log_2(n))=2k, then a(n) = 2^k.
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EXAMPLE
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a(50)=floor(50/a(25))
..... a(25)=floor(25/a(12))
........... a(12)=floor(12/a(6))
................. a(6)=floor(6/a(3))
...................... a(3)=floor(3/a(1))
........................... a(1)=1
...................... a(3)=floor(3/a(1))=floor(3/1)=3
................. a(6)=floor(6/a(3))=floor(6/3)=2
........... a(12)=floor(12/a(6))=floor(12/2)=6
..... a(25)=floor(25/a(12))=floor(25/6)=4
a(50)=floor(50/a(25))=floor(50/4)=12.
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MAPLE
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f:= proc(n) option remember; floor(n/procname(floor(n/2))) end proc:
f(1):= 1:
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = Floor[n/a[Floor[n/2]]]; Table[ a[n], {n, 94}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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