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

%I

%S 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,

%T 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,

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

%N The minimum absolute difference between k*p1 and p2 (p1<p2), where p1*p2 is the n-th term of A087112.

%C 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.

%H Lei Zhou, <a href="/A254606/b254606.txt">Table of n, a(n) for n = 1..10000</a>

%e A087112(1)=4=2*2, 2-2=0, so a(1)=0;

%e A087112(2)=6=2*3, 3-2=2*2-3=1, so a(2)=1;

%e ...

%e A087112(9)=35=5*7, 7-5=2, and 2*5-7=3, the smaller is 2. So a(9)=2.

%t 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]]];

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

%Y Cf. A087112, A254605.

%K nonn,easy

%O 1,9

%A _Lei Zhou_, Feb 02 2015

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Last modified January 23 13:57 EST 2022. Contains 350511 sequences. (Running on oeis4.)