OFFSET
1,1
COMMENTS
The fractions having these numerators slowly converge to Pi. The 1000th term at 2000-digit precision yields 3.1400...
REFERENCES
John Derbshire, Prime Obsession, 2004, Joseph Henry Press, p. 16.
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..1000
EXAMPLE
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.
MATHEMATICA
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 *)
PROG
(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)", ") ) }
CROSSREFS
KEYWORD
easy,frac,nonn
AUTHOR
Cino Hilliard, Jan 09 2006
STATUS
approved