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Numbers k such that 0 and 5 occur juxtaposed in the base-10 representation of k but not of k+1.
1

%I #12 Aug 27 2021 11:05:55

%S 50,105,150,205,250,305,350,405,450,509,550,605,650,705,750,805,850,

%T 905,950,1005,1059,1105,1150,1205,1250,1305,1350,1405,1450,1509,1550,

%U 1605,1650,1705,1750,1805,1850,1905,1950,2005,2059

%N Numbers k such that 0 and 5 occur juxtaposed in the base-10 representation of k but not of k+1.

%H Michael De Vlieger, <a href="/A044000/b044000.txt">Table of n, a(n) for n = 1..10000</a>

%t With[{j = 0, k = 5}, Position[Partition[Array[Boole[Total@ {SequenceCount[#, {j, k}], SequenceCount[#, {k, j}]} > 0] &@ IntegerDigits[#] &, 2100], 2, 1], {1, 0}][[All, 1]]] (* _Michael De Vlieger_, Aug 27 2021 *)

%K nonn,base

%O 1,1

%A _Clark Kimberling_