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 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. 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 (list; graph; refs; listen; history; text; internal format)
 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 := 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

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)