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Numbers n such that string 0,1 occurs in the base 9 representation of n but not of n+1.
0

%I #10 Jan 16 2024 18:16:12

%S 82,163,244,325,406,487,568,649,730,746,811,892,973,1054,1135,1216,

%T 1297,1378,1459,1475,1540,1621,1702,1783,1864,1945,2026,2107,2188,

%U 2204,2269,2350,2431,2512,2593,2674,2755,2836,2917

%N Numbers n such that string 0,1 occurs in the base 9 representation of n but not of n+1.

%t Select[Range[3000],MemberQ[Partition[IntegerDigits[#,9],2,1],{0,1}] && !MemberQ[ Partition[IntegerDigits[#+1,9],2,1],{0,1}]&] (* _Harvey P. Dale_, Feb 20 2013 *)

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,9],{0,1}]>0,1,0],{n,3000}],{1,0}] [[;;,1]] (* _Harvey P. Dale_, Jan 16 2024 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_