A227127 - OEIS

%I #16 Jul 09 2013 06:59:28

%S 1,1,2,8,20,12,28,16,36,60,22,72,52,28,60,96,102,36,114,80,42,132,92,

%T 144,200,104,54,112,58,120,434,128,198,68,350,72,222,228,156,240,246,

%U 84,430,88,180,92,564,576,196,100,204,312,106,540,330,336,342,116,354,240,122

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

%C 1/A008578(n) and successive rows:

%C 1,          1/2,     1/3,     1/5,   1/7,

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

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

%C 3/10,  -136/105,

%C 67/42

%C b(n) is essentially A006094. See A209329.

%C 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,... .

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

%e 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.

%e a(3) = 4*2 = 8, a(4) = 5*4 = 20.

%t 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 *)

%Y Cf. A002110, A006954.

%K nonn,frac

%O 0,3

%A _Paul Curtz_, Jul 02 2013