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Numbers n such that string 0,2 occurs in the base 4 representation of n but not of n+1.
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%I #7 Oct 15 2016 12:29:40

%S 18,34,50,66,75,82,98,114,130,139,146,162,178,194,203,210,226,242,258,

%T 267,274,303,306,322,331,338,354,370,386,395,402,418,434,450,459,466,

%U 482,498,514,523,530,559,562,578,587,594,610

%N Numbers n such that string 0,2 occurs in the base 4 representation of n but not of n+1.

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,4],{0,2}]>0,1,0],{n,700}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 15 2016 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_