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A297139 Numbers whose base-7 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 A297139 #10 Jan 18 2018 07:24:51
%S A297139 1,2,3,4,5,6,8,16,24,32,40,48,49,56,57,58,59,60,61,62,65,73,81,89,97,
%T A297139 98,106,112,113,114,115,116,117,118,122,130,138,146,147,155,163,168,
%U A297139 169,170,171,172,173,174,179,187,195,196,204,212,220,224,225,226
%N A297139 Numbers whose base-7 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 A297139 These numbers comprise the complement of the set of numbers in the union of A297137 and A297138.
%C A297139 Differs from A044818 first for 344 = 1001_7. 1001_7 has two runs of length 1 and is not in A044818, but it has a sequence of two consecutive zeros and is in this sequence. - _R. J. Mathar_, Jan 18 2018
%e A297139 Base-7 digits of 4998: 2,0,4,0,0, so that 4998 is in the sequence.
%p A297139 read("transforms") :
%p A297139 isA297139 := proc(n)
%p A297139         local dgs,ud;
%p A297139         dgs := convert(n,base,7) ;
%p A297139         if nops(dgs) < 2 then
%p A297139                 return true;
%p A297139         end if;
%p A297139         if 0 in DIFF(dgs) then
%p A297139                 true;
%p A297139         else
%p A297139                 false;
%p A297139         end if;
%p A297139 end proc:
%p A297139 for n from 1 to 300 do
%p A297139         if isA297139(n) then
%p A297139                 printf("%d,",n) ;
%p A297139         end if;
%p A297139 end do: # _R. J. Mathar_, Jan 18 2018
%t A297139 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297139 b = 7; t = Table[a[n, b], {n, 1, 10*z}];
%t A297139 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297137 *)
%t A297139 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297138 *)
%t A297139 Complement[Range[z], Union[u, v]]  (* A297139 *)
%Y A297139 Cf. A297137, A297138.
%K A297139 nonn,easy,base
%O A297139 1,2
%A A297139 _Clark Kimberling_, Jan 15 2018