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A081885
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Number of steps needed to reach an integer starting with n+1/16 and iterating the map x-->x*ceiling(x).
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0
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8, 5, 3, 8, 18, 8, 5, 6, 5, 6, 3, 6, 7, 5, 1, 6, 4, 6, 3, 4, 2, 6, 2, 7, 3, 2, 4, 6, 2, 5, 1, 8, 12, 4, 7, 4, 8, 7, 3, 9, 10, 5, 3, 9, 5, 6, 1, 3, 11, 4, 2, 4, 4, 4, 2, 4, 6, 7, 2, 2, 5, 3, 1, 7, 9, 9, 5, 7, 4, 13, 4, 5, 6, 8, 6, 14, 8, 3, 1, 4, 2, 5, 4, 5, 3, 2, 2, 10, 2, 5, 3, 18, 4, 3, 1, 11, 4, 7, 7, 4, 5
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OFFSET
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1,1
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COMMENTS
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Conjecture : let b(n,m) denotes the number of steps needed to reach an integer starting with n+1/2^m and iterating the map x-->x*ceiling(x); then sum(k=1,n,b(k,m)) is asymptotic to (m+1)*n.
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LINKS
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FORMULA
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It seems that sum(k=1, n, a(k)) is asymptotic to 5n.
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MATHEMATICA
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Table[Length[NestWhileList[# Ceiling[#]&, n+1/16, !IntegerQ[#]&]]-1, {n, 110}] (* Harvey P. Dale, Apr 02 2012 *)
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PROG
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(PARI) a(n)=if(n<0, 0, s=n+1/16; c=0; while(frac(s)>0, s=s*ceil(s); c++); c)
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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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