A297140 Numbers having an up-first zigzag pattern in base 8; see Comments.

10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122

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 A297140-A297142 partition the natural numbers. See the guide at A297146.

Links

Table of n, a(n) for n=1..59.

Example

Base-8 digits of 3575: 6, 7, 6, 7, with pattern UDU, so that 3575 is in the sequence.

Mathematica

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 8; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297140 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297141 *)
Complement[Range[z], Union[u, v]]  (* A297142 *)

Crossrefs

Cf. A297141, A297142.

Sequence in context: A174397 A297266 A296707 * A173688 A008709 A008708

Adjacent sequences: A297137 A297138 A297139 * A297141 A297142 A297143

Keyword

nonn,easy,base

Author

Clark Kimberling, Jan 15 2018

Status

approved