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A073339
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Define b(k) by the recursion b(1)=n, b(k+1)=b(k)-trunc(k/b(k)), where trunc(x) is floor(x) for x>=0, ceiling(x) for x<0. Sequence gives the value a(n) such that b(a(n))=0; if k>a(n) then b(k) is undefined.
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1
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2, 5, 5, 69, 69, 12, 69, 69, 69, 29, 69, 19, 69, 69, 29, 29, 631, 28, 30, 631, 69, 69, 69, 631, 72, 42, 1167, 631, 72, 631, 631, 1167, 51, 631, 1167, 631, 631, 1167, 102, 103, 69, 1167, 1167, 69, 72, 631, 631, 631, 631, 1167, 631, 130, 631, 83, 631, 1167, 631
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OFFSET
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1,1
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COMMENTS
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By definition a(n)>n. Conjecture: a(n) is always defined. Often the b sequences for two values of n merge and a(n) is the same for both values. So some numbers, such as 69, 631, 1167 and 689027, occur in the sequence more often than others.
Is sum(k=1,n,a(k))/(n^2*log(n)) bounded?
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LINKS
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MATHEMATICA
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trunc[x_] := If[x>0, Floor[x], Ceiling[x]]; a[n_] := Module[{k, b}, For[k=0; b=n, b!=0, k++, b-=trunc[k/b]]; k]
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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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