login
Least m>0 such that (2*n-1)!!+m and (2*n)!!-m are not relatively prime.
1

%I #4 Jul 27 2012 21:35:02

%S 2,8,3,3,1,3,3,3,1,3,1,3,3,3,1,3,3,3,3,3,1,3,3,3,3,3,3,3,3,3,3,3,1,3,

%T 1,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,3,1,3,3,3,

%U 3,3,3,3,3,3,1,3,3,3,3,3,1,3,1,3,3,3,3,3,1,3,3,3,3,3,3,3,3,3,3

%N Least m>0 such that (2*n-1)!!+m and (2*n)!!-m are not relatively prime.

%H Clark Kimberling, <a href="/A214072/b214072.txt">Table of n, a(n) for n = 1..1000</a>

%e gcd(15+1,48-1) = 1, gcd(15+2,48-2) = 1, gcd(15+3,48-3) > 1, so that a(3) = 3.

%t b[n_] := (2 n - 1)!!; c[n_] := (2 n)!!;

%t Table[m = 1; While[GCD[b[n] + m, c[n] - m] == 1, m++]; m, {n, 1, 140}]

%Y Cf. A214054.

%K nonn,easy

%O 1,1

%A _Clark Kimberling_, Jul 26 2012