A032523 - OEIS

%I #35 Apr 04 2015 10:03:18

%S 4,9,1,30,40,32,2,44,130,100,276,55,28,13,3,78,647,137,140,180,214,83,

%T 203,91,791,112,574,175,243,147,878,455,531,421,1008,594,784,3041,721,

%U 1872,754,119,492,429,81,3200,825,283,3027,465,1437,3384,1547,1864,446

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

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

%C 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

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

%C 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

%H M. F. Hasler and Eric W. Weisstein, <a href="/A032523/b032523.txt">Table of n, a(n) for n = 1..47086</a> (terms n = 1..3131 from _M. F. Hasler_, using data from H. Havermann)

%H H. Havermann, <a href="http://chesswanks.com/seq/picf-fop.txt">24345 terms of a trivial variation (first term of Pi excluded) of A032523</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>

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

%F A032523(n) = min { k | A001203(k)=n }. - _M. F. Hasler_, Mar 31 2008

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

%o (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

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

%Y Cf. A001203, A107892, A138758, A138759.

%K nonn,nice,look

%O 1,1

%A _Wouter Meeussen_

%E Edited by _M. F. Hasler_, Mar 31 2008