A227127 The Akiyama-Tanigawa algorithm applied to 1/(1,2,3,5,... old prime numbers). Reduced numerators of the second row.

1, 1, 2, 8, 20, 12, 28, 16, 36, 60, 22, 72, 52, 28, 60, 96, 102, 36, 114, 80, 42, 132, 92, 144, 200, 104, 54, 112, 58, 120, 434, 128, 198, 68, 350, 72, 222, 228, 156, 240, 246, 84, 430, 88, 180, 92, 564, 576, 196, 100, 204, 312, 106, 540, 330, 336, 342, 116, 354, 240, 122

Offset: 0

Author

Paul Curtz, Jul 02 2013

Keywords

• nonn
• frac

Comments

1/A008578(n) and successive rows:

1, 1/2, 1/3, 1/5, 1/7,

1/2, 1/3, 2/5, 8/35, = c(n) = a(n)/b(n)

1/6, -2/15, 18/35,

3/10, -136/105,

67/42

b(n) is essentially A006094. See A209329.

a(n) yields to a permutation of A008578 (via 1, 1, 2, 8, 12, 16, 20, 22, ...): 1, 2, 3, 5, 11, 17, 7, 29,... .

Examples

			a(n) is the numerators of c(n): c(0) = 1-1/2 = 1/2, c(1) = 2*(1/2-1/3) = 1/3, c(2) = 3*(1/3-1/5) = 2/5, c(3) = 4*(1/5-1/7)=8/35.
a(3) = 4*2 = 8, a(4) = 5*4 = 20.
		

Crossrefs

Cf. A002110, A006954.

Programs

Mathematica

a[0, 0] = 1; a[0, m_ /; m > 0] := 1/Prime[m]; a[n_, m_] := a[n, m] = (m+1)*(a[n-1, m ] - a[n-1, m+1]); Table[a[1, m] // Numerator, {m, 0, 60}] (* Jean-François Alcover, Jul 04 2013 *)

Formula

a(n) = (n+1)*A001223(n-1), for n>=3.