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Quarter-squares greedy Champernowne sequence (or word): write the numbers 0, 1, 10, 11, 100, 101, as in A376450 and concatenate.
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%I #4 Sep 30 2024 12:39:58

%S 0,1,0,1,0,1,0,1,0,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,0,1,0,1,

%T 0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1,0,0,1,0,1,0,1,0,1,0,1,0,1,

%U 0,1,0,1,0,1,0,1,0,1,0,1,0,0,1,0,1,0,1

%N Quarter-squares greedy Champernowne sequence (or word): write the numbers 0, 1, 10, 11, 100, 101, as in A376450 and concatenate.

%C The quarter-square base is A002620 = (1,2,4,6,9,12,16,...), in which 15 = 12 + 2 + 1, written in quarter-square base as 100011, which contributes 1,0,0,1,1 to this sequence.

%t greedy[list_, n_] := Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, n, Reverse[list]]][[2, 1]];

%t seq = Table[Floor[((n + 1)^2)/4], {n, 30}]; (* A002620 *)

%t t1 = Table[FromDigits[greedy[seq, n]], {n, Last[seq]}];

%t d = Map[Last, Map[First, RealDigits[t1, 10]]]

%t (* _Peter J. C. Moses_, Oct 18 2012; from A214973 *)

%Y Cf. A002620, A376450, A376452, A376453.

%K nonn,base

%O 0

%A _Clark Kimberling_, Sep 28 2024