A128060 a(n) = 2*n - numerator((2*n-1)^2/(2*(2*n)!)).

-1, 1, 1, 1, 1, 9, 1, 1, 15, 1, 1, 21, 1, 25, 27, 1, 1, 33, 35, 1, 39, 1, 1, 45, 1, 49, 51, 1, 55, 57, 1, 1, 63, 65, 1, 69, 1, 1, 75, 77, 1, 81, 1, 85, 87, 1, 91, 93, 95, 1, 99, 1, 1, 105, 1, 1, 111, 1, 115, 117, 119, 121, 123, 125, 1, 129, 1, 133, 135, 1, 1, 141, 143, 145, 147

Offset: 0

Author

Paul Barry, Feb 13 2007

Keywords

• easy
• sign

Comments

Odd composite numbers with placeholders for primes between them.

Links

• Ivan V. Morozov, On Quotients of a More General Theorem of Wilson, arXiv:2505.16201 [math.NT], 2025. See denominators of Z+ p. 9.

Crossrefs

Cf. A128059, A160479, A217983.

Programs

Maple

A128060 := proc(n): 2*n - numer((2*n-1)^2/(2*(2*n)!)) end: seq(A128060(n), n=0..62);
# End program 1 [Johannes W. Meijer, Oct 25 2012]
A128060 := proc(n) local n1: n1:=2*n-1: if type(n1, prime) then A128060(n) := 1 else A128060(n) := n1 fi: end: seq(A128060(n), n=0..62);
# End program 2 [Johannes W. Meijer, Oct 25 2012]

Mathematica

Table[2n - Numerator[(2n - 1)^2/(2(2n)!)], {n, 0, 74}] (* Alonso del Arte, Jan 05 2014 *)

Formula

a(n) = 2*n - A128059(n).

a(n) = (A217983(n-1) * (2*n-1))/A160479(n) for n >= 3. - Johannes W. Meijer, Oct 25 2012

a(0) = -1, a(n) = gcd(2*n-1, (2*n-2)!), n > 0. - Wesley Ivan Hurt, Jan 05 2014

Extensions

More terms from Michel Marcus, May 23 2025