A000319 - OEIS

%I #37 Mar 01 2025 08:37:13

%S 1,1,74,-1,-2,-3,0,1,30,-2,-2,29,1,4,-6,0,1,2,-1,-1,-1,-1,-2,-9,0,0,1,

%T 2,-2,-35,-1,-1,-1,-1,-1,-1,-1,-2,-3,0,0,1,5,-2,-2,3,1,1,-4,-1,-1,-1,

%U -1,-1,-1,-1,-1,-2,-3,1,2,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-2,-3,0,1,2,-1,-2,-21,-7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0

%N a(n) = floor(b(n)), where b(n) = tan(b(n-1)), b(0)=1.

%C Using 3000-digit precision, interval arithmetic provides an efficient method of computing over 2000000 terms of this sequence. The iteration is stopped when an interval contains an integer. So far, no term equals 319. - _T. D. Noe_, Mar 07 2008

%C The question whether 319 occurs is relevant for sequences A053169 and A053873. - _Antti Karttunen_ and _M. F. Hasler_, Mar 01 2025

%H T. D. Noe, <a href="/A000319/b000319.txt">Table of n, a(n) for n = 0..10000</a>

%e From _José María Grau Ribas_, Apr 13 2010: (Start)

%e For n=2, tan(tan(1)) = 74.68... (A085665), so a(2)=74.

%e For n=3, tan(tan(tan(1))) = -0.8635... (A085666), so a(3)=-1. (End)

%t Floor[Table[Nest[Tan, 1, n], {n, 1, 200}]] (* _José María Grau Ribas_, Apr 13 2010 *)

%Y See A381230 (resp. A381231) for when n (resp. -n) appears.

%Y Cf. A053169, A053873, A085665, A085666.

%K sign,changed

%O 0,3

%A _N. J. A. Sloane_