A214055 Least m>0 such that n!+2+m and n-m have a common divisor > 1.

1, 2, 3, 1, 5, 2, 1, 2, 9, 1, 11, 2, 1, 2, 15, 1, 17, 2, 1, 2, 21, 1, 3, 2, 1, 2, 27, 1, 29, 2, 1, 2, 3, 1, 35, 2, 1, 2, 39, 1, 41, 2, 1, 2, 45, 1, 5, 2, 1, 2, 51, 1, 3, 2, 1, 2, 57, 1, 59, 2, 1, 2, 3, 1, 65, 2, 1, 2, 69, 1, 71, 2, 1, 2, 5, 1, 77, 2, 1, 2

Offset: 1

Author

Clark Kimberling, Jul 22 2012

Keywords

• nonn
• easy

Examples

			6!+2+1=723, 6-1=5; 6!+2+2=724, 6-2=4; so a(6)=2.
		

Links

• Clark Kimberling, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A020639, A060680.

Programs

Mathematica

b[n_] := n! + 2; c[n_] := n; Table[m = 1; While[GCD[b[n] + m, c[n] - m] == 1, m++]; m, {n, 100}]