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Numbers n such that string 1,1 occurs in the base 9 representation of n but not of n-1.
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%I #10 Aug 03 2021 11:34:05

%S 10,90,172,253,334,415,496,577,658,739,810,901,982,1063,1144,1225,

%T 1306,1387,1468,1548,1630,1711,1792,1873,1954,2035,2116,2197,2277,

%U 2359,2440,2521,2602,2683,2764,2845,2926,3006,3088

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

%t Select[Range[3100],MemberQ[Partition[IntegerDigits[#,9],2,1],{1,1}] && !MemberQ[Partition[IntegerDigits[#-1,9],2,1],{1,1}]&] (* _Harvey P. Dale_, Mar 01 2012 *)

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,9],{1,1}]>0,1,0],{n,3100}],{0,1}][[All,2]] (* _Harvey P. Dale_, Aug 03 2021 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_