A381231 -id:A381231 - cp's OEIS frontend

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

Offset: 0

N. J. A. Sloane

sign

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

			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)

T. D. Noe, Table of n, a(n) for n = 0..10000
Tim Peters, CSV table of a(n) for n = 0..7366317 in "value,count" format

See A381230 (resp. A381231) for when n (resp. -n) appears.
Cf. A053169, A053873, A085665, A085666.
Cf. A000329 (with round).

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

A381230 Index of first occurrence of n in A000319, or -1 if n never appears there.

Original entry on oeis.org

6, 0, 17, 45, 13, 42, 938, 920, 57403, 7865, 15862, 313445, 54988, 53976, 57573, 61372, 83445, 14998, 360213, 57322, 59858, 2070497, 2021631, 14918, 58001, 1394543, 79664, 2056395, 85989, 11, 8, 71662, 5495575, 5652770, 360110, 2070250, 5947332, 5514279, 5514772, 2015129, 78877, 305403, 1031, 1869352, 5652707, 4823241

Offset: 0

N. J. A. Sloane, Feb 28 2025

nonn

If a(57) is not -1, then a(57) > 14333074. - Tim Peters, Mar 13 2025

			0 is the 6th term of A000319, so a(0) = 6. 1 is the 0th term, so a(1) = 0.

Tim Peters, Table of n, a(n) for n = 0..56

Cf. A000319, A381231.

a(8)-a(10) from Hugo Pfoertner, Feb 28 2025
a(11)-a(31) from Tim Peters, Mar 01 2025
a(32) from Tim Peters, Mar 02 2025
a(33)-a(45) from Tim Peters, Mar 04 2025

cp's OEIS Frontend

A000319 a(n) = floor(b(n)), where b(n) = tan(b(n-1)), b(0)=1.

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