cp's OEIS Frontend

A297125 Numbers having a down-first zigzag pattern in base 3; see Comments.

%I A297125 #9 Apr 11 2018 09:02:30
%S A297125 3,6,7,10,11,19,20,21,23,30,32,33,34,57,59,60,61,64,65,69,70,91,92,96,
%T A297125 97,100,101,102,104,172,173,177,178,181,182,183,185,192,194,195,196,
%U A297125 208,209,210,212,273,275,276,277,289,290,291,293,300,302,303,304
%N A297125 Numbers having a down-first zigzag pattern in base 3; see Comments.
%C A297125 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 A297124..A297127 partition the natural numbers.  See the guide at A297146.
%e A297125 Base-3 digits of 307: 1,0,2,1,0,1, with pattern DUDU, so that 307 is in the sequence.
%t A297125 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297125 b = 3; t = Table[a[n, b], {n, 1, 10*z}];
%t A297125 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297124 *)
%t A297125 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297125 *)
%t A297125 Complement[Range[z], Union[u, v]]  (* A297126 *)
%Y A297125 Cf. A297124, A297126.
%K A297125 nonn,easy,base
%O A297125 1,1
%A A297125 _Clark Kimberling_, Jan 13 2018