A000319 - OEIS

A000319

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

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, 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, -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

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OFFSET

0,3

COMMENTS

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

The question whether 319 occurs is relevant for sequences A053169 and A053873. - Antti Karttunen and M. F. Hasler, Mar 01 2025

LINKS

T. D. Noe, Table of n, a(n) for n = 0..10000

EXAMPLE

From José María Grau Ribas, Apr 13 2010: (Start)

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

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

MATHEMATICA

Floor[Table[Nest[Tan, 1, n], {n, 1, 200}]] (* José María Grau Ribas, Apr 13 2010 *)

CROSSREFS

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

Cf. A053169, A053873, A085665, A085666.