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Numbers n such that string 1,3 occurs in the base 5 representation of n but not of n+1.
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%I #8 Nov 21 2013 12:47:03

%S 8,33,44,58,83,108,133,158,169,183,224,233,258,283,294,308,333,358,

%T 383,408,419,433,458,483,508,533,544,558,583,608,633,658,669,683,708,

%U 733,758,783,794,808,849,858,883,908,919,933,958

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

%t Select[Range[1000],MemberQ[Partition[IntegerDigits[#,5],2,1],{1,3}]&&!MemberQ[Partition[IntegerDigits[#+1,5],2,1],{1,3}]&] (* _Harvey P. Dale_, Mar 11 2011 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_