This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A203168 #24 Feb 16 2025 08:33:16 %S A203168 4,6,7,8,10,12,15,16,21,24,25,29,35,41,42,45,47,51,53,54,56,57,58,60, %T A203168 61,63,64,66,68,69,74,79,82,84,87,89,92,94,96,98,99,104,108,113,115, %U A203168 116,121,125,126,134,136,138,141,144,148,149,150,154,157,158,160 %N A203168 Positions of 1 in the continued fraction expansion of Pi. %C A203168 In the Gauss-Kuzmin distribution, 1 appears with probability log_2(4/3) = 41.5037...%. Thus the n-th appearance of 1 in the continued fraction of a real number chosen uniformly from [0, 1) will be, with probability 1, n / (log_2(4/3)) + O(sqrt(n)). Does this sequence have the same asymptotic? - _Charles R Greathouse IV_, Dec 30 2011 %H A203168 T. D. Noe, <a href="/A203168/b203168.txt">Table of n, a(n) for n = 1..1000</a> %H A203168 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a> %H A203168 <a href="/index/Con#confC">Index entries for continued fractions for constants</a> %H A203168 <a href="/index/Ph#Pi314">Index entries for sequences related to the number Pi</a> %F A203168 A001203(a(n)) = 1. %t A203168 Flatten[Position[ContinuedFraction[Pi, 160], 1]] %o A203168 (PARI) v=contfrac(Pi);for(i=1,#v,if(v[i]==1,print1(i", "))) \\ _Charles R Greathouse IV_, Dec 30 2011 %Y A203168 Cf. A001203, A033089, A000796. %K A203168 nonn,nice %O A203168 1,1 %A A203168 _Ben Branman_, Dec 29 2011