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A225802 Position of first occurrence of n in continued fraction for Pi, or -1 if n never occurs.

%I A225802 #17 Feb 16 2025 08:33:19
%S A225802 3,8,0,29,39,31,1,43,129,99,275,54,27,12,2,77,646,136,139,179,213,82,
%T A225802 202,90,790,111,573,174,242,146,877,454,530,420,1007,593,783,3040,720,
%U A225802 1871,753,118,491,428,80,3199,824,282,3026,464,1436,3383,1546,1863,445,1017
%N A225802 Position of first occurrence of n in continued fraction for Pi, or -1 if n never occurs.
%C A225802 Correctly indexed version of A032523.
%C A225802 All positive integers <= 49003 occur in the first 15000000000 terms of the c.f. (the first that do not are 49004, 50471, 53486, 56315, 58255, ...) - _Eric W. Weisstein_, Jul 27 2013
%H A225802 Eric W. Weisstein, <a href="/A225802/b225802.txt">Table of n, a(n) for n = 1..49003</a>
%H A225802 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PiContinuedFraction.html">Pi Continued Fraction</a>
%F A225802 a(n) = A032523(n) - 1.
%e A225802 The continued fraction of Pi is [a_0; a_1, a_2, ...] = [3; 7, 15, 1, 292, 1, 1, 1, 2, 1, ...], so
%e A225802 a(1) = 3 (1 first occurs at term a_3);
%e A225802 a(2) = 8 (2 first occurs at term a_8);
%e A225802 a(3) = 0 (3 first occurs at term a_0).
%Y A225802 Cf. A032523 (= a(n) + 1).
%Y A225802 Cf. A001203 (continued fraction of Pi).
%K A225802 nonn
%O A225802 1,1
%A A225802 _Eric W. Weisstein_, Jul 27 2013
%E A225802 "Escape clause" added to definition by _Jianing Song_, Apr 06 2019