

A254606


The minimum absolute difference between k*p1 and p2 (p1<p2), where p1*p2 is the nth term of A087112.


3



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
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OFFSET

1,9


COMMENTS

k is an integer that minimizes k*p1p2. It is trivial that if j is the integer part of p2/p1, k is either j or j+1.


LINKS



EXAMPLE

A087112(1)=4=2*2, 22=0, so a(1)=0;
A087112(2)=6=2*3, 32=2*23=1, so a(2)=1;
...
A087112(9)=35=5*7, 75=2, and 2*57=3, the smaller is 2. So a(9)=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 = 2; p2 = 1; Table[p2 = NextPrime[p2]; If[p2 > p1, p1 = p2; p2 = 2]; NumDiff[p1, p2], {n, 1, 100}]


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



