W. Lang Aug 29 2007

Rationals r(n)= A132049(n)/A132050(n), with

r(n):=2*n*e(n-1)/e(n) where e(n):=A000111(n), ("zig-zag" numbers).

See the J.-P. Delahaye reference given in A132049.

Rationals in lowest terms.

r(n), n=3,...,23:

[3, 16/5, 25/8, 192/61, 427/136, 4352/1385, 12465/3968, 158720/50521, 555731/176896,
 8491008/2702765, 817115/260096, 626311168/199360981, 2990414715/951878656, 60920233984/19391512145, 
329655706465/104932671488, 7555152347136/2404879675441, 45692713833379/14544442556416, 
232711080902656/74074237647505, 7777794952988025/2475749026562048, 
217865914337460224/69348874393137901, 1595024111042171723/507711943253426176, 
48740346552328912896/15514534163557086905, 387863354088927172625/123460740095103991808]


The values for n=1 and 2 are r(1)=2 and r(2)=4. 

The values r(10^k),k=0,..,3 are: (maple11, 10 dgits)

[2., 3.141663863, 3.141592654]

This should be compared with Pi (maple11, 10 digits)

3.141592654 .


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