A254605 The minimum absolute difference between k*m1 and m2 (m1A075362.

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

Offset: 1

Author

Lei Zhou, Feb 02 2015

Keywords

• nonn
• easy

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.

Examples

			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.
		

Links

• Lei Zhou, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A075362, A022267.

Programs

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}]