This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A083094 #39 Jun 27 2025 01:06:29
%S A083094 0,8,20,24,56,60,72,80,164,168,180,188,216,224,236,240,488,492,504,
%T A083094 512,540,548,560,564,648,656,668,672,704,708,720,728,1460,1464,1476,
%U A083094 1484,1512,1520,1532,1536,1620,1628,1640,1644,1676,1680,1692,1700,1944,1952
%N A083094 Numbers k such that Sum_{j=0..k} (binomial(k,j) mod 3) is odd.
%C A083094 Apparently a(n)/2 (mod 3) = A010060(n), the Thue-Morse sequence.
%F A083094 a(n) = 4*A083095(n). - _Hugo Pfoertner_, Jan 12 2025
%F A083094 Numbers that are multiples of 4 and such that base-3 digits contain no 1's, or equivalently, numbers such that base-3 digits contains an even number of 2's and no 1's, i.e. a(n) = 2*A074939(n-1). This characterization can be derived from the formula in A051638. - _Chai Wah Wu_, Jun 26 2025
%t A083094 Select[Range[0, 2000],OddQ[Sum[Mod[Binomial[#, j], 3], {j, 0, #}]] &] (* _Paul F. Marrero Romero_, Dec 28 2024 *)
%o A083094 (PARI) isok(n) = sum(k=0, n, binomial(n,k) % 3) % 2; \\ _Michel Marcus_, Dec 05 2013
%o A083094 (Python)
%o A083094 def A083094(n): return int(bin(((m:=n-1).bit_count()&1)+(m<<1))[2:],3)<<1 # _Chai Wah Wu_, Jun 26 2025
%Y A083094 Cf. A010060, A051638, A074939, A083093, A083095 (gives a b-file of 16384 terms).
%K A083094 easy,nonn
%O A083094 1,2
%A A083094 _Benoit Cloitre_, Apr 22 2003
%E A083094 More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Apr 29 2003