A254606 The minimum absolute difference between k*p1 and p2 (p1A087112.

0, 1, 0, 1, 1, 0, 1, 1, 2, 0, 1, 1, 1, 3, 0, 1, 1, 2, 1, 2, 0, 1, 1, 2, 3, 5, 4, 0, 1, 1, 1, 2, 3, 6, 2, 0, 1, 1, 2, 2, 1, 3, 6, 4, 0, 1, 1, 1, 1, 4, 3, 5, 9, 6, 0, 1, 1, 1, 3, 2, 5, 3, 7, 8, 2, 0, 1, 1, 2, 2, 4, 2, 3, 1, 9, 8, 6, 0, 1, 1, 1, 1, 3, 2, 7, 3, 5

Offset: 1

Author

Lei Zhou, Feb 02 2015

Keywords

• nonn
• easy

Comments

k is an integer that minimizes |k*p1-p2|. It is trivial that if j is the integer part of p2/p1, k is either j or j+1.

Examples

			A087112(1)=4=2*2, 2-2=0, so a(1)=0;
A087112(2)=6=2*3, 3-2=2*2-3=1, so a(2)=1;
...
A087112(9)=35=5*7, 7-5=2, and 2*5-7=3, the smaller is 2. So a(9)=2.
		

Links

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

Crossrefs

Cf. A087112, A254605.

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 = 2; p2 = 1; Table[p2 = NextPrime[p2]; If[p2 > p1, p1 = p2; p2 = 2]; NumDiff[p1, p2], {n, 1, 100}]