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A227127 The Akiyama-Tanigawa algorithm applied to 1/(1,2,3,5,... old prime numbers). Reduced numerators of the second row. 0
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 (list; graph; refs; listen; history; text; internal format)
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-Fran├žois 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

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Last modified September 23 07:26 EDT 2021. Contains 347609 sequences. (Running on oeis4.)