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

3, 6, 7, 10, 11, 19, 20, 21, 23, 30, 32, 33, 34, 57, 59, 60, 61, 64, 65, 69, 70, 91, 92, 96, 97, 100, 101, 102, 104, 172, 173, 177, 178, 181, 182, 183, 185, 192, 194, 195, 196, 208, 209, 210, 212, 273, 275, 276, 277, 289, 290, 291, 293, 300, 302, 303, 304

Offset

1,1

Comments

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.

Links

Table of n, a(n) for n=1..57.

Example

Base-3 digits of 307: 1,0,2,1,0,1, with pattern DUDU, so that 307 is in the sequence.

Mathematica

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 3; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297124 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297125 *)
Complement[Range[z], Union[u, v]]  (* A297126 *)

Crossrefs

Cf. A297124, A297126.

Sequence in context: A087249 A188073 A286806 * A211969 A173059 A189387

Adjacent sequences: A297122 A297123 A297124 * A297126 A297127 A297128

Keyword

nonn,easy,base

Author

Clark Kimberling, Jan 13 2018

Status

approved