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A154883
Distinct entries in continued fraction for Pi in the order of their appearance.
4
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
OFFSET
1,1
COMMENTS
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
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 1..1000, May 06 2013
EXAMPLE
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, ...
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 continued fraction), A322778 (inverse), A033090.
Sequence in context: A128658 A234042 A001203 * A302029 A109732 A349183
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