A254605 The minimum absolute difference between k*m1 and m2 (m1<m2), where m1*m2 is the n-th term of A075362.

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

1,19

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