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Numbers n such that string 5,3 occurs in the base 9 representation of n but not of n+1.
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%I #7 Aug 25 2019 16:31:09

%S 48,129,210,291,372,440,453,534,615,696,777,858,939,1020,1101,1169,

%T 1182,1263,1344,1425,1506,1587,1668,1749,1830,1898,1911,1992,2073,

%U 2154,2235,2316,2397,2478,2559,2627,2640,2721,2802

%N Numbers n such that string 5,3 occurs in the base 9 representation of n but not of n+1.

%t SequencePosition[Table[If[SequenceCount[IntegerDigits[n,9],{5,3}]>0,1,0],{n,3000}],{1,0}][[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Aug 25 2019 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_