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Numbers k such that 1 and 3 occur juxtaposed in the base-4 representation of k but not of k+1.
1

%I #13 Aug 25 2021 04:53:14

%S 7,13,23,31,39,45,55,61,71,77,87,95,103,109,127,135,141,151,159,167,

%T 173,183,189,199,205,223,231,237,247,253,263,269,279,287,295,301,311,

%U 317,327,333,343,351,359,365,383,391,397,407,415

%N Numbers k such that 1 and 3 occur juxtaposed in the base-4 representation of k but not of k+1.

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,4],{1,3}]>0 || SequenceCount[IntegerDigits[n,4],{3,1}]>0,1,0],{n,500}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, May 13 2020 *)

%Y Cf. A007090.

%K nonn,base

%O 1,1

%A _Clark Kimberling_