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A214057 Least m>0 such that 2^n-1+m and n-m have a common divisor > 1. 3

%I

%S 1,2,1,4,1,3,1,8,1,10,1,3,1,14,1,16,1,3,1,5,1,2,1,3,1,26,1,28,1,3,1,4,

%T 1,6,1,2,1,15,1,5,1,2,1,5,1,17,1,3,1,50,1,8,1,2,1,56,1,58,1,3,1,2,1,6,

%U 1,3,1,31,1,70,1,3,1,4,1,6,1,3,1,5,1,2,1

%N Least m>0 such that 2^n-1+m and n-m have a common divisor > 1.

%H Clark Kimberling, <a href="/A214057/b214057.txt">Table of n, a(n) for n = 1..1000</a>

%e gcd(2^6-1-1,6-1) = gcd(62,5) = 1

%e gcd(2^6-1-2,6-2) = gcd(61,4) = 1

%e gcd(2^6-1-3,6-3) = gcd(60,3) = 3,

%e so that a(6) = 3.

%t b[n_] := 2^n-1; c[n_] := n;

%t Table[m = 1; While[GCD[b[n] + m, c[n] - m] == 1, m++]; m, {n, 1, 100}]

%Y Cf. A214056.

%K nonn,easy

%O 1,2

%A _Clark Kimberling_, Jul 22 2012

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Last modified May 9 18:53 EDT 2021. Contains 343744 sequences. (Running on oeis4.)