A257886 Least positive m such that floor(n! / (2*(floor(n/2)!))) + m is prime.

2, 1, 2, 1, 1, 1, 1, 13, 1, 1, 29, 1, 1, 37, 29, 17, 31, 71, 71, 37, 23, 1, 37, 1, 41, 41, 31, 31, 59, 31, 41, 41, 41, 41, 41, 37, 41, 193, 83, 41, 53, 67, 149, 97, 59, 73, 113, 107, 137, 59, 137, 67, 101, 83, 73, 101, 241, 71, 73, 79, 83, 227, 199, 223, 127, 83, 83, 181, 227, 149, 103, 1, 587, 179, 229, 167, 127, 163, 109, 83

Offset: 1

Author

David Morales Marciel, May 11 2015

Keywords

• nonn

Comments

Conjecture: No term is composite (similar conjecture to A033932 for a different expression).

Examples

			n = 1, floor(1! / (2*(floor(1/2)!)))=0, m = 2, and 0+2=2 is prime.
n = 2, floor(2! / (2*(floor(2/2)!)))=1, m = 1, and 1+1=2 is prime.
...
n = 15, floor(15! / (2*(floor(15/2)!)))=129729600, m = 29, and 129729600+29 = 129729629 is prime.
		

Links

• David Morales Marciel, About Fortunate numbers and other similar expressions

Crossrefs

Cf. A033932.

Programs

Mathematica

lpm[n_]:=Module[{c=Floor[n!/(2Floor[n/2]!)]},NextPrime[c]-c]; Array[lpm,80] (* Harvey P. Dale, May 15 2018 *)

Python

from sympy import factorial, nextprime
[(nextprime(int(factorial(n)/(2*factorial(n//2)))))-int(factorial(n)/(2*factorial(n//2))) for n in range(1,10**5)]

Extensions

Edited. Wolfdieter Lang, Jun 08 2015