A066160 - OEIS

%I #20 Sep 08 2022 08:45:04

%S 1,6,8,15,18,21,27,35,38,42,53,56,60,63,68,71,77,78,83,90,95,110,116,

%T 117,122,125,137,147,161,162,165,180,188,203,207,215,221,227,228,230,

%U 242,243,246,258,260,266,276,291,293,306,308,315,320,321

%N Numbers n such that 4n-1 divides (2n-1)! - 1.

%H Harry J. Smith, <a href="/A066160/b066160.txt">Table of n, a(n) for n=1..1000</a>

%H Ed Pegg, Jr., <a href="http://www.mathpuzzle.com/25Feb.htm">Math. Puzzles</a> (Material added Dec 11 2001)

%p A066160:=n->`if`((2*n-1)! - 1 mod (4*n-1) = 0, n, NULL): seq(A066160(n), n=1..500); # _Wesley Ivan Hurt_, Dec 01 2015

%t Select[Range[350], Mod[(2 # - 1)! - 1, 4 # - 1] == 0 &] (* _Vincenzo Librandi_, Dec 02 2015 *)

%o (PARI) { n=0; for (m=1, 10^9, if (frac(((2*m - 1)! - 1)/(4*m - 1)) == 0, write("b066160.txt", n++, " ", m); if (n==1000, return)) ) } \\ _Harry J. Smith_, Feb 03 2010

%o (Magma) [n: n in [1..350] |  (Factorial(2*n-1)-1) mod(4*n-1) eq 0]; // _Vincenzo Librandi_, Dec 02 2015

%Y Cf. A066159.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Dec 13 2001