

A032523


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


15



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
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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 * A032760 A129970 A006830
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



