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A297142 Numbers whose base-8 digits d(m), d(m-1),..., d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,...,m-1}.

%I A297142 #8 Jan 18 2018 07:38:16
%S A297142 1,2,3,4,5,6,7,9,18,27,36,45,54,63,64,72,73,74,75,76,77,78,79,82,91,
%T A297142 100,109,118,127,128,137,144,145,146,147,148,149,150,151,155,164,173,
%U A297142 182,191,192,201,210,216,217,218,219,220,221,222,223,228,237,246
%N A297142 Numbers whose base-8 digits d(m), d(m-1),..., d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,...,m-1}.
%C A297142 These numbers comprise the complement of the set of numbers in the union of A297140 and A297141.
%C A297142 Differs from A044819 first for 513 = 1001_8, which has two consecutive equal digits and is in this sequence, but has two runs of equal length (1), and is not in A044819. - _R. J. Mathar_, Jan 17 2018
%e A297142 Base-8 digits of 5000: 1,1,6,1,0, so that 5000 is in the sequence.
%p A297142 read("transforms") :
%p A297142 isA297142 := proc(n)
%p A297142     local dgs,ud;
%p A297142     dgs := convert(n,base,8) ;
%p A297142     if nops(dgs) < 2 then
%p A297142         return true;
%p A297142     end if;
%p A297142     if 0 in DIFF(dgs) then
%p A297142         true;
%p A297142     else
%p A297142         false;
%p A297142     end if;
%p A297142 end proc:
%p A297142 for n from 1 to 300 do
%p A297142     if isA297142(n) then
%p A297142         printf("%d,",n) ;
%p A297142     end if;
%p A297142 end do: # _R. J. Mathar_, Jan 18 2018
%t A297142 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297142 b = 8; t = Table[a[n, b], {n, 1, 10*z}];
%t A297142 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297140 *)
%t A297142 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297141 *)
%t A297142 Complement[Range[z], Union[u, v]]  (* A297142 *)
%Y A297142 Cf. A297140, A297142.
%K A297142 nonn,easy,base
%O A297142 1,2
%A A297142 _Clark Kimberling_, Jan 15 2018