

A113479


Starting with the fraction 4/1 as the first term, a(n) is the numerator of the reduced fraction of the nth 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.


1



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

1,1


COMMENTS

The fractions having these numerators slowly converge to Pi. The 1000th term at 2000 digits 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 A103970 A227295
Adjacent sequences: A113476 A113477 A113478 * A113480 A113481 A113482


KEYWORD

easy,frac,nonn


AUTHOR

Cino Hilliard, Jan 09 2006


STATUS

approved



