

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
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OFFSET

1,1


COMMENTS

A onetoone 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, i1, 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



