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

0,3

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,... .

Links

Table of n, a(n) for n=0..60.

Formula

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

Example

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.

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 *)

Crossrefs

Cf. A002110, A006954.

Sequence in context: A129445 A082821 A188893 * A227399 A327098 A030097

Adjacent sequences: A227124 A227125 A227126 * A227128 A227129 A227130

Keyword

nonn,frac

Author

Paul Curtz, Jul 02 2013

Status

approved