A364447 Repeat [1,2,1,3].

1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1, 2, 1, 3, 1

Offset: 1

Author

Rok Cestnik, Jul 25 2023

Keywords

• nonn
• easy

Comments

Continued fraction of sqrt(5) - 3/2 = 0.7360679... (without integer part); and (4*sqrt(5) + 6)/11 = 1.3585701... (with integer part).

Lexicographically earliest sequence in which n is banned for n terms after each appearance (see A364448 for n^2 and A364449 for n^3).

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Crossrefs

Cf. A131743 (repeat [0,1,0,2]).

Cf. A000034, A010882, A131534.

Cf. A364448, A364449.

Programs

Mathematica

PadRight[{}, 100, {1, 2, 1, 3}] (* Paolo Xausa, Jan 23 2025 *)

Python

def A364447(n): return (3,1,2,1)[n&3] # Chai Wah Wu, Jul 29 2023

Formula

a(n) = A131743(n-1) + 1.