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%I #21 May 15 2018 12:14:11
%S 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,
%T 31,59,31,41,41,41,41,41,37,41,193,83,41,53,67,149,97,59,73,113,107,
%U 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
%N Least positive m such that floor(n! / (2*(floor(n/2)!))) + m is prime.
%C Conjecture: No term is composite (similar conjecture to A033932 for a different expression).
%H David Morales Marciel, <a href="http://hobbymaths.blogspot.jp/2015/05/about-fortunate-numbers-and-other.html">About Fortunate numbers and other similar expressions</a>
%e n = 1, floor(1! / (2*(floor(1/2)!)))=0, m = 2, and 0+2=2 is prime.
%e n = 2, floor(2! / (2*(floor(2/2)!)))=1, m = 1, and 1+1=2 is prime.
%e ...
%e n = 15, floor(15! / (2*(floor(15/2)!)))=129729600, m = 29, and 129729600+29 = 129729629 is prime.
%t lpm[n_]:=Module[{c=Floor[n!/(2Floor[n/2]!)]},NextPrime[c]-c]; Array[lpm,80] (* _Harvey P. Dale_, May 15 2018 *)
%o (Python)
%o from sympy import factorial, nextprime
%o [(nextprime(int(factorial(n)/(2*factorial(n//2)))))-int(factorial(n)/(2*factorial(n//2))) for n in range(1,10**5)]
%Y Cf. A033932.
%K nonn
%O 1,1
%A _David Morales Marciel_, May 11 2015
%E Edited. _Wolfdieter Lang_, Jun 08 2015