A113479 - OEIS

%I #11 Jan 14 2021 21:14:46

%S 4,8,32,128,256,512,4096,32768,65536,131072,524288,2097152,4194304,

%T 8388608,134217728,2147483648,4294967296,8589934592,34359738368,

%U 137438953472,274877906944,549755813888,4398046511104,35184372088832

%N Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the n-th term according to the rule: if n is even, multiply the previous term by n/(n+1); otherwise multiply the previous term by (n+1)/n.

%C The fractions having these numerators slowly converge to Pi. The 1000th term at 2000-digit precision yields 3.1400...

%D John Derbshire, Prime Obsession, 2004, Joseph Henry Press, p. 16.

%H G. C. Greubel, <a href="/A113479/b113479.txt">Table of n, a(n) for n = 1..1000</a>

%e The first term is 4/1. Then the 2nd term is 4/1*2/(2 + 1) = 8/3. So 8 is the 2nd entry in the table.

%t a[1] := 4; a[n_] := a[n] = If[EvenQ[n], n*a[n - 1]/(n + 1), (n + 1)*a[n - 1]/n]; Numerator[Table[a[n], {n, 1, 50}]] (* _G. C. Greubel_, Mar 12 2017 *)

%o (PARI) g(n) = { a=4;b=1; print1(4","); for(x=2,n, if(x%2==0,a=a*x;b=b*(x+1),a=a*(x+1);b=b*x); print1(numerator(a/b)",") ) }

%K easy,frac,nonn

%O 1,1

%A _Cino Hilliard_, Jan 09 2006