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A154883
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Distinct entries in continued fraction for Pi in the order of their appearance.
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4
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3, 7, 15, 1, 292, 2, 14, 84, 13, 4, 6, 99, 5, 8, 12, 16, 161, 45, 22, 24, 10, 26, 42, 9, 57, 18, 19, 30, 28, 20, 120, 23, 21, 127, 29, 11, 48, 436, 58, 34, 44, 20776, 94, 55, 32, 50, 43, 72, 33, 27, 36, 106, 17, 141, 39, 125, 41, 37, 25, 47, 61, 376, 107, 31
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OFFSET
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1,1
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COMMENTS
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This is presumably a permutation of the positive integers. The inverse permutation (or "index sequence") A322778 begins 4,6,1,10,13,11,2,14,... and gives the position in the continued fraction of Pi at which 1, 2, 3, 4, 5, 6, ... first appear. - Remark corrected by N. J. A. Sloane, Jan 04 2019
The name means that when a number not yet in this sequence appears in the continued fraction of Pi, then that number is added to the sequence. - T. D. Noe, May 06 2013
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LINKS
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EXAMPLE
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Since the actual continued fraction for Pi is 3, 7, 15, 1, 292, 1, 1, 1, 2, ..., this sequence begins 3, 7, 15, 1, 292, 2, ...
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MATHEMATICA
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DeleteDuplicates[ContinuedFraction[Pi, 1000]] (* Harvey P. Dale, May 06 2013 *)
t = {}; s = ContinuedFraction[Pi, 1000]; Do[If[! MemberQ[t, s[[n]]], AppendTo[t, s[[n]]]], {n, Length[s]}]; t (* T. D. Noe, May 06 2013 *)
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PROG
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(PARI) \p 10000
v=contfrac(Pi); for(i=1, #v, for(j=1, i-1, if(v[i]==v[j], v[i]=0; break))); v=select(n->n, v) \\ Charles R Greathouse IV, May 06 2013
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CROSSREFS
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KEYWORD
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nice,nonn
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AUTHOR
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Lee Corbin (lcorbin(AT)rawbw.com), Jan 16 2009
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EXTENSIONS
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STATUS
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approved
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