cp's OEIS Frontend

A297138 Numbers having a down-first zigzag pattern in base 7; see Comments.

%I A297138 #7 Apr 11 2018 09:02:49
%S A297138 7,14,15,21,22,23,28,29,30,31,35,36,37,38,39,42,43,44,45,46,47,50,51,
%T A297138 52,53,54,55,99,100,101,102,103,104,105,107,108,109,110,111,148,149,
%U A297138 150,151,152,153,154,156,157,158,159,160,161,162,164,165,166,167
%N A297138 Numbers having a down-first zigzag pattern in base 7; see Comments.
%C A297138 A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense.  Writing U for up and D for down, there are two kinds of patterns:  U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... .  In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b".  Example:    2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern.  The sequences A297137-A297139 partition the natural numbers.  See the guide at A297146.
%e A297138 Base-7 digits of 5000: 2,0,4,0,2, with pattern DUDU, so that 5000 is in the sequence.
%t A297138 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297138 b = 7; t = Table[a[n, b], {n, 1, 10*z}];
%t A297138 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297137 *)
%t A297138 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297138 *)
%t A297138 Complement[Range[z], Union[u, v]]  (* A297139 *)
%Y A297138 Cf. A297137, A297139.
%K A297138 nonn,easy,base
%O A297138 1,1
%A A297138 _Clark Kimberling_, Jan 15 2018