A154883 Distinct entries in continued fraction for Pi in the order of their appearance.

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

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