A113479 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.

4, 8, 32, 128, 256, 512, 4096, 32768, 65536, 131072, 524288, 2097152, 4194304, 8388608, 134217728, 2147483648, 4294967296, 8589934592, 34359738368, 137438953472, 274877906944, 549755813888, 4398046511104, 35184372088832

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

Sequence in context: A241684 A254878 A247473 * A252540 A327493 A103970

Adjacent sequences: A113476 A113477 A113478 * A113480 A113481 A113482

Keyword

easy,frac,nonn

Author

Cino Hilliard, Jan 09 2006

Status

approved