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A154883 Nonrepeated entries in continued fraction for pi. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 1..1000

EXAMPLE

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, ...

MATHEMATICA

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 *)

PROG

(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

CROSSREFS

Cf. A001203, A033089 (for records of main CF), A033090.

Sequence in context: A128658 A234042 A001203 * A109732 A114396 A102032

Adjacent sequences:  A154880 A154881 A154882 * A154884 A154885 A154886

KEYWORD

nice,nonn

AUTHOR

Lee Corbin (lcorbin(AT)rawbw.com), Jan 16 2009

EXTENSIONS

More terms from Harvey P. Dale, May 05 2013

STATUS

approved

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Last modified April 24 12:50 EDT 2014. Contains 240983 sequences.