A005699 -id:A005699 - cp's OEIS frontend

A005657 a(n) = floor( tan(n)^2 ).

0, 2, 4, 0, 1, 11, 0, 0, 46, 0, 0, 51053, 0, 0, 52, 0, 0, 12, 1, 0, 5, 2, 0, 2, 4, 0, 1, 10, 0, 0, 41, 0, 0, 5672, 0, 0, 60, 0, 0, 13, 1, 0, 5, 2, 0, 2, 4, 0, 1, 10, 0, 0, 36, 0, 0, 2041, 0, 0, 69, 0, 0, 14, 1, 0, 5, 2, 0, 2, 4, 0, 1, 9, 0, 0, 32, 0, 0, 1041, 0, 0, 81, 0, 0, 15, 1, 0, 5, 2, 0, 2, 3, 0, 1, 8, 0, 0, 29, 0, 0, 629

Offset: 0

N. J. A. Sloane

Robert Israel, Table of n, a(n) for n = 0..10000
R. K. Guy & N. J. A. Sloane, Correspondence, 1985

Cf. A000503, A005699.

[Floor(Tan(n)^2): n in [0..100]]; // Vincenzo Librandi, Jun 15 2015

seq(floor(tan(n)^2),n=0..1000); # Robert Israel, Jun 14 2015

Floor[Tan[Range[0,70]]^2] (* Harvey P. Dale, Nov 06 2011 *)

vector(100, n, n--; floor(tan(n)^2)) \\ Michel Marcus, Jun 15 2015

a(n) = A005699(n)-1 for n >= 1.

A381238 a(n) = floor(b(n)), where b(n) = sec^2(b(n-1)), b(0)=1.

Original entry on oeis.org

1, 3, 1, 4, 66, 1, 11, 4, 8, 3, 1, 6, 1, 143, 2, 1, 481, 10, 14, 6, 1, 4, 11, 2, 1, 140, 3, 1, 3, 1, 7, 14, 2, 2, 1, 3, 1, 39, 3, 1, 2159, 3, 1, 4, 3, 1, 3, 1, 14, 10, 1, 11, 6, 1, 3, 1, 4, 185, 1, 3, 1, 4, 78, 1, 3, 1, 6, 1, 4, 3, 2, 2, 1, 11, 17, 8, 15, 1, 16, 5, 1, 14, 4, 8, 7, 1, 20, 7, 96, 14, 62, 1, 3, 2, 2, 1, 91, 1, 10, 97, 1

Offset: 0

N. J. A. Sloane, Mar 17 2025

nonn

a(0)-a(100) were computed using Maple with 10000 digits of precision.
A variant of A000319 (note that sec(x)^2 is the derivative of tan(x)).
Conjecture: Every nonnegative number appears in this sequence. (See A382148.)

Paolo Xausa, Table of n, a(n) for n = 0..1000

Cf. A000319, A005699, A382148.

Floor[NestList[Sec[#]^2 &, 1, 100]] (* Paolo Xausa, Mar 18 2025 *)

cp's OEIS Frontend

A005657 a(n) = floor( tan(n)^2 ).

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