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A384602 Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 2, where T is the Wythoff array (A035513).

%I A384602 #11 Jun 26 2025 01:20:49
%S A384602 1,10,16,25,34,40,49,55,64,73,79,88,103,112,118,127,136,142,151,166,
%T A384602 175,181,190,205,214,220,229,238,244,253,268,277,283,292,301,307,316,
%U A384602 331,340,346,355,370,379,385,394,403,409,418,433,442,448,457,466,472
%N A384602 Numbers k such that T(k, 1) mod 3 = 1 and T(k, 2) mod 3 = 2, where T is the Wythoff array (A035513).
%C A384602 This is one of 9 sets that partition the positive integers; see the Jun 04 2025 comment in A035513.
%e A384602 (Row 10 of T) = (25, 41, 66, 107, ...)
%e A384602 ((Row 10 of T) mod 3) = (1, 2, 0, 2, ...), so 10 is in the list.
%t A384602 w[n_] := {Floor[n*GoldenRatio] + n - 1, 2*Floor[n*GoldenRatio] + n - 1}
%t A384602 t = Table[Mod[w[n], 3], {n, 1, 500}];
%t A384602 Flatten[Position[t, {1, 1}]]   (* A384601 *)
%t A384602 Flatten[Position[t, {1, 2}]]   (* A384602 *)
%Y A384602 Cf. A035513, A384601.
%K A384602 nonn
%O A384602 1,2
%A A384602 _Clark Kimberling_, Jun 06 2025