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A384601 Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 1, where T is the Wythoff array (A035513).

%I A384601 #15 Jun 26 2025 01:20:57
%S A384601 2,8,17,26,32,41,56,65,71,80,89,95,104,110,119,128,134,143,158,167,
%T A384601 173,182,191,197,206,221,230,236,245,260,269,275,284,293,299,308,323,
%U A384601 332,338,347,356,362,371,377,386,395,401,410,425,434,440,449,458,464
%N A384601 Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 1, where T is the Wythoff array (A035513).
%C A384601 This is one of 9 sets that partition the positive integers; see the Jun 04 2025 comment in A035513.
%e A384601 (Row 8 of T) = (19,31,50,81,...).
%e A384601 ((Row 8 of T) mod 3) = (1,1,2,0,...), so 8 is in the list.
%t A384601 w[n_] := {Floor[n*GoldenRatio] + n - 1, 2*Floor[n*GoldenRatio] + n - 1}
%t A384601 t = Table[Mod[w[n], 3], {n, 1, 500}];
%t A384601 Flatten[Position[t, {1, 1}]]   (* A384601 *)
%t A384601 Flatten[Position[t, {1, 2}]]   (* A384602 *)
%Y A384601 Cf. A035513, A384602.
%K A384601 nonn
%O A384601 1,1
%A A384601 _Clark Kimberling_, Jun 05 2025