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A254605
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The minimum absolute difference between k*m1 and m2 (m1<m2), where m1*m2 is the n-th term of A075362.
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2
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0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 0, 2, 1, 0, 0, 1, 1, 1, 2, 1, 0, 0, 0, 1, 0, 2, 2, 1, 0, 0, 1, 0, 1, 1, 3, 2, 1, 0, 0, 0, 1, 2, 0, 2, 3, 2, 1, 0, 0, 1, 1, 1, 1, 1, 3, 3, 2, 1, 0, 0, 0, 0, 0, 2, 0, 2, 4, 3, 2, 1, 0, 0, 1, 1, 1, 2, 1, 1, 3, 4
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OFFSET
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1,19
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COMMENTS
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k is an integer that minimizes |k*m1-m2|. It is trivial that if j is the integer part of m2/m1, k is either j or j+1.
Interestingly, suppose b is the smallest n such that a(n)=c; the sequence s(c)=b is then sequence A022267.
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LINKS
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EXAMPLE
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A075362(1)=1=1*1, 1-1=0, so a(1)=0;
A075362(5)=6=2*3, 3-2=1, 2*2-3=1, so a(5)=1;
A075362(19)=24=4*6, 6-4=2, 4*2-6=2, so a(19)=2.
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MATHEMATICA
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NumDiff[n1_, n2_] := Module[{c1 = n1, c2 = n2}, If[c1 < c2, c1 = c1 + c2; c2 = c1 - c2; c1 = c1 - c2];
k = Floor[c1/c2]; a1 = c1 - k*c2; If[a1 == 0, a2 = 0, a2 = (k + 1) c2 - c1]; Return[Min[a1, a2]]];
p1 = 1; p2 = 0; Table[p2++; If[p2 > p1, p1 = p2; p2 = 1]; NumDiff[p1, p2], {n, 1, 100}]
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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