A242569 n!-2n.

-1, -2, 0, 16, 110, 708, 5026, 40304, 362862, 3628780, 39916778, 479001576, 6227020774, 87178291172, 1307674367970, 20922789887968, 355687428095966, 6402373705727964, 121645100408831962, 2432902008176639960, 51090942171709439958, 1124000727777607679956, 25852016738884976639954, 620448401733239439359952

Offset: 1

Author

Derek Orr, May 17 2014

Keywords

• sign

Comments

For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is an integer.

For n > 2, a(n) is the largest value of k such that (n!+k)/(n+k) is prime.

For n > 1, a(n) is even.

Examples

			3!-2*3 = 0 so a(3) = 0.
4!-2*4 = 16 so a(4) = 16.
5!-2*5 = 110 so a(5) = 110.
		

Crossrefs

Cf. A000142, A242567, A242568.

Programs

Mathematica

Table[n!-2n,{n,30}] (* Harvey P. Dale, Oct 22 2024 *)

PARI

for(n=1,25,print(n!-2*n))

Python

import math
{print(math.factorial(n)-2*n) for n in range(1,25)}

Formula

a(n) = n!-2n.