A297128 Numbers having an up-first zigzag pattern in base 4; see Comments.

6, 7, 11, 24, 25, 27, 28, 29, 30, 44, 45, 46, 97, 98, 99, 100, 102, 103, 108, 109, 110, 113, 114, 115, 116, 118, 119, 120, 121, 123, 177, 178, 179, 180, 182, 183, 184, 185, 187, 388, 390, 391, 392, 393, 395, 396, 397, 398, 401, 402, 403, 408, 409, 411, 412

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 A297128..A297130 partition the natural numbers. See the guide at A297146.

Links

Table of n, a(n) for n=1..55.

Example

Base-4 digits of 3003: 2,3,2,3,2,3, with pattern UDUDU, so that 3003 is in the sequence.

Mathematica

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 4; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297128 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297129 *)
Complement[Range[z], Union[u, v]]  (* A297130 *)

Crossrefs

Cf. A297129, A297130.

Sequence in context: A347512 A296695 A228948 * A035110 A011990 A105085

Adjacent sequences: A297125 A297126 A297127 * A297129 A297130 A297131

Keyword

nonn,easy,base

Author

Clark Kimberling, Jan 13 2018

Status

approved