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

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

Author

N. J. A. Sloane, Mar 17 2025

Keywords

• nonn

Comments

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.)

Links

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

Crossrefs

Cf. A000319, A005699, A382148.

Programs

Mathematica

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