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A154883
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Nonrepeated entries in continued fraction for pi.
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1
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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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A one-to-one map of the natural numbers into themselves and so also generates a "partner sequence" or "index sequence" 4 6 1 10 13 11 2 14 24 21 36 30 33 19 32 20 ? 22 ? 29 35 28 ... which notes the place in the continued fraction of pi in which 1, 2, 3, 4, 5, 6,... make their appearance (see A??????).
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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Charles R Greathouse IV, Table of n, a(n) for n = 1..1000
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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 must be 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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Cf. A001203, A033089 (for records of main CF), A033090.
Sequence in context: A106363 A128658 A001203 * A109732 A114396 A102032
Adjacent sequences: A154880 A154881 A154882 * A154884 A154885 A154886
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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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More terms from Harvey P. Dale, May 05 2013
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STATUS
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approved
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