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A043107 Numbers k such that 0 and 2 occur juxtaposed in the base-5 representation of k but not of k-1.

%I A043107 #13 Aug 22 2021 16:13:55
%S A043107 10,27,35,50,60,77,85,102,110,127,135,152,160,175,185,202,210,227,235,
%T A043107 250,277,285,300,310,327,335,352,360,377,385,402,410,425,435,452,460,
%U A043107 477,485,502,510,527,535,550,560,577,585,602
%N A043107 Numbers k such that 0 and 2 occur juxtaposed in the base-5 representation of k but not of k-1.
%H A043107 Robert Israel, <a href="/A043107/b043107.txt">Table of n, a(n) for n = 1..10000</a>
%p A043107 has02:= proc(n) local L,i,state;
%p A043107   L:= convert(n,base,5);
%p A043107   state:= 1;
%p A043107   for i from 1 to nops(L) do
%p A043107     if L[i] = 0 then
%p A043107       if state = 2 then return true
%p A043107       else state:= 0
%p A043107       fi
%p A043107     elif L[i] = 2 then
%p A043107       if state = 0 then return true
%p A043107       else state:= 2
%p A043107       fi
%p A043107     else state:= 1;
%p A043107     fi
%p A043107   od;
%p A043107   false
%p A043107 end proc:
%p A043107 H:= select(has02, {$1..1001}):
%p A043107 sort(convert(H minus map(`+`,H,1),list)); # _Robert Israel_, Jan 20 2019
%t A043107 With[{s = Partition[Array[IntegerDigits[#, 5] &, 602], 2, 1]}, Map[FromDigits[#, 5] &, Select[s, And[And[SequenceCount[#1, {0, 2}] == 0, SequenceCount[#1, {2, 0}] == 0], Or[SequenceCount[#2, {0, 2}] > 0, SequenceCount[#2, {2, 0}] > 0]] & @@ # &][[All, -1]] ] ] (* _Michael De Vlieger_, Jan 20 2019 *)
%Y A043107 Cf. A007091.
%K A043107 nonn,base
%O A043107 1,1
%A A043107 _Clark Kimberling_