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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
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)
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).
Sequence in context: A152205 A129861 A055491 * A350623 A032760 A129970
KEYWORD
nonn,nice,look
EXTENSIONS
Edited by M. F. Hasler, Mar 31 2008
STATUS
approved