cp's OEIS Frontend

A297131 Numbers having an up-first zigzag pattern in base 5; see Comments.

%I A297131 #6 Jan 14 2018 23:01:36
%S A297131 7,8,9,13,14,19,35,36,38,39,40,41,42,44,45,46,47,48,65,66,67,69,70,71,
%T A297131 72,73,95,96,97,98,176,177,178,179,180,182,183,184,190,191,192,194,
%U A297131 195,196,197,198,201,202,203,204,205,207,208,209,210,211,213,214
%N A297131 Numbers having an up-first zigzag pattern in base 5; see Comments.
%C A297131 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 A297131-A297133 partition the natural numbers.  See the guide at A297146.
%e A297131 Base-5 digits of 4973: 1,2,4,3,4,3, with pattern UDUD, so that 4973 is in the sequence.
%t A297131 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297131 b = 5; t = Table[a[n, b], {n, 1, 10*z}];
%t A297131 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297131 *)
%t A297131 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297132 *)
%t A297131 Complement[Range[z], Union[u, v]]  (* A297133 *)
%Y A297131 Cf. A297132, A297133.
%K A297131 nonn,easy,base
%O A297131 1,1
%A A297131 _Clark Kimberling_, Jan 14 2018