A083095 a(n) = A083094(n)/4.

0, 2, 5, 6, 14, 15, 18, 20, 41, 42, 45, 47, 54, 56, 59, 60, 122, 123, 126, 128, 135, 137, 140, 141, 162, 164, 167, 168, 176, 177, 180, 182, 365, 366, 369, 371, 378, 380, 383, 384, 405, 407, 410, 411, 419, 420, 423, 425, 486, 488, 491, 492, 500

Offset: 1

Author

Benoit Cloitre, Apr 22 2003

Keywords

• nonn
• easy

Comments

Is this the same as A083097? - Andrew S. Plewe, May 30 2007

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..16384 (terms 1..106 from Paul F. Marrero Romero)

Crossrefs

Cf. A010060, A051638, A083093, A083094, A083097, A074939.

Programs

Mathematica

Select[Range[0,2000], OddQ[Sum[Mod[Binomial[#,j],3],{j,0,#}]]&]/4 (* Paul F. Marrero Romero, Dec 28 2024 *)

Python

def A083095(n): return int(bin(((m:=n-1).bit_count()&1)+(m<<1))[2:],3)>>1 # Chai Wah Wu, Jun 26 2025

Formula

Apparently (2*a(n)) mod 3 = A010060(n-1), the Thue-Morse sequence.

Numbers k such that C(4*k, 2*k) == 1 (mod 3). - Benoit Cloitre, Jul 30 2003

Numbers k such that the base-3 digits of 2k contains no 2's, i.e. a(n) = A074939(n-1)/2. - Chai Wah Wu, Jun 26 2025

Extensions

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003