A254605 - OEIS

%I #14 Mar 19 2015 07:12:12

%S 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,

%T 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,

%U 0,0,2,0,2,4,3,2,1,0,0,1,1,1,2,1,1,3,4

%N The minimum absolute difference between k*m1 and m2 (m1<m2), where m1*m2 is the n-th term of A075362.

%C 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.

%C Interestingly, suppose b is the smallest n such that a(n)=c; the sequence s(c)=b is then sequence A022267.

%H Lei Zhou, <a href="/A254605/b254605.txt">Table of n, a(n) for n = 1..10000</a>

%e A075362(1)=1=1*1, 1-1=0, so a(1)=0;

%e A075362(5)=6=2*3, 3-2=1, 2*2-3=1, so a(5)=1;

%e A075362(19)=24=4*6, 6-4=2, 4*2-6=2, so a(19)=2.

%t NumDiff[n1_, n2_] :=  Module[{c1 = n1, c2 = n2}, If[c1 < c2, c1 = c1 + c2; c2 = c1 - c2; c1 = c1 - c2];

%t   k = Floor[c1/c2]; a1 = c1 - k*c2; If[a1 == 0, a2 = 0, a2 = (k + 1) c2 - c1]; Return[Min[a1, a2]]];

%t p1 = 1; p2 = 0; Table[p2++; If[p2 > p1, p1 = p2; p2 = 1];  NumDiff[p1, p2], {n, 1, 100}]

%Y Cf. A075362, A022267.

%K nonn,easy

%O 1,19

%A _Lei Zhou_, Feb 02 2015