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A233582
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Coefficients of the generalized continued fraction expansion Pi = a(1) +a(1)/(a(2) +a(2)/(a(3) +a(3)/(a(4) +a(4)/....))).
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12
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3, 21, 111, 113, 158, 160, 211, 216, 525, 1634, 1721, 7063, 8771, 15077, 26168, 58447, 223767, 254729, 587278, 1046086, 1491449, 1635223, 1689171, 2039096, 2290214, 13444599, 22666443, 1276179737, 4470200748
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OFFSET
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1,1
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COMMENTS
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Definition of "Blazys" generalized continued fraction expansion of an irrational real number x>1:
Set n=1,r=x; (ii) set a(n)=floor(r); (iii) set r=a(n)/(r-a(n)); (iv) increment n and iterate from point (ii).
For the inverse of this mapping, see A233588.
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LINKS
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FORMULA
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Pi = 3+3/(21+21/(111+111/(113+113/(158+...)))).
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MATHEMATICA
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BlazysExpansion[n_, mx_] := Block[{k = 1, x = n, lmt = mx + 1, s, lst = {}}, While[k < lmt, s = Floor[x]; x = 1/(x/s - 1); AppendTo[lst, s]; k++]; lst]; BlazysExpansion[Pi, 33] (* Robert G. Wilson v, May 22 2014 *)
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PROG
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(PARI) bx(x, nmax)={local(c, v, k);
v = vector(nmax); c = x; for(k=1, nmax, v[k] = floor(c); c = v[k]/(c-v[k]); ); return (v); }
bx(Pi, 1000) \\ Execution; use very high real precision
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CROSSREFS
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KEYWORD
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nonn,cofr
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AUTHOR
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STATUS
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approved
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