A032523 Index of first occurrence of n as a term in A001203, the continued fraction for Pi.

4, 9, 1, 30, 40, 32, 2, 44, 130, 100, 276, 55, 28, 13, 3, 78, 647, 137, 140, 180, 214, 83, 203, 91, 791, 112, 574, 175, 243, 147, 878, 455, 531, 421, 1008, 594, 784, 3041, 721, 1872, 754, 119, 492, 429, 81, 3200, 825, 283, 3027, 465, 1437, 3384, 1547, 1864, 446

Offset

1,1

Comments

Incorrectly indexed version of A225802 (assuming the c.f. is [a_1; a_2, a_3, ...] instead of [a_0; a_1, a_2, ...]).

Until it is proved that every integer n>0 does occur in A001203, we should tacitly understand a convention like "A032523(n) = 0 if n does not occur in A001203". - M. F. Hasler, Mar 31 2008

All positive integers <= 33674 occur in the first 5,821,569,425 terms of the c.f. - Eric W. Weisstein, Sep 19 2011

All positive integers <= 47086 occur in the first 10,672,905,501 terms of the c.f. (the first that do not are 47087, 49004, 50465, 50471, ...) - Eric W. Weisstein, Jul 18 2013

Links

M. F. Hasler and Eric W. Weisstein, Table of n, a(n) for n = 1..47086 (terms n = 1..3131 from M. F. Hasler, using data from H. Havermann)

H. Havermann, 24345 terms of a trivial variation (first term of Pi excluded) of A032523

Eric Weisstein's World of Mathematics, Pi Continued Fraction

Formula

a(n) = A225802(n) + 1.

A032523(n) = min { k | A001203(k)=n }. - M. F. Hasler, Mar 31 2008

Mathematica

With[{cfp=ContinuedFraction[Pi, 5000]}, Flatten[Table[Position[cfp, n, 1, 1], {n, 60}]]] (* Harvey P. Dale, Dec 11 2012 *)

Prog

(PARI) default( realprecision, 15000); v=contfrac(Pi); a(n) = for( i=1, #v, v[i]==n && return(i)) \\ - W. Meeussen, simplified by M. F. Hasler, Mar 31 2008

Crossrefs

Cf. A225802 (= a(n) - 1).

Cf. A001203, A107892, A138758, A138759.

Sequence in context: A152205 A129861 A055491 * A350623 A032760 A129970

Adjacent sequences: A032520 A032521 A032522 * A032524 A032525 A032526

Keyword

nonn,nice,look

Author

Wouter Meeussen

Extensions

Edited by M. F. Hasler, Mar 31 2008

Status

approved