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 A254605 The minimum absolute difference between k*m1 and m2 (m1
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,19 COMMENTS 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. LINKS Lei Zhou, Table of n, a(n) for n = 1..10000 EXAMPLE 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. MATHEMATICA 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}] CROSSREFS Cf. A075362, A022267. Sequence in context: A204770 A333382 A143379 * A335664 A269518 A219840 Adjacent sequences:  A254602 A254603 A254604 * A254606 A254607 A254608 KEYWORD nonn,easy AUTHOR Lei Zhou, Feb 02 2015 STATUS approved

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Last modified December 7 20:40 EST 2021. Contains 349589 sequences. (Running on oeis4.)