A043107 - OEIS

%I #13 Aug 22 2021 16:13:55

%S 10,27,35,50,60,77,85,102,110,127,135,152,160,175,185,202,210,227,235,

%T 250,277,285,300,310,327,335,352,360,377,385,402,410,425,435,452,460,

%U 477,485,502,510,527,535,550,560,577,585,602

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

%H Robert Israel, <a href="/A043107/b043107.txt">Table of n, a(n) for n = 1..10000</a>

%p has02:= proc(n) local L,i,state;

%p   L:= convert(n,base,5);

%p   state:= 1;

%p   for i from 1 to nops(L) do

%p     if L[i] = 0 then

%p       if state = 2 then return true

%p       else state:= 0

%p       fi

%p     elif L[i] = 2 then

%p       if state = 0 then return true

%p       else state:= 2

%p       fi

%p     else state:= 1;

%p     fi

%p   od;

%p   false

%p end proc:

%p H:= select(has02, {$1..1001}):

%p sort(convert(H minus map(`+`,H,1),list)); # _Robert Israel_, Jan 20 2019

%t 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 Cf. A007091.

%K nonn,base

%O 1,1

%A _Clark Kimberling_