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A297146 Numbers having an up-first zigzag pattern in base 10; see Comments. 17
12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145 (list; graph; refs; listen; history; text; internal format)
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 A297146-A297148 partition the natural numbers. In the following guide, column four, "complement" means the sequence of natural numbers not in the corresponding sequences in columns 2 and 3.

***

Base      up-first    down-first  complement

2           (none)     A000975     A107907

3          A297124     A297125     A297126

4          A297128     A297129     A297130

5          A297131     A297132     A297133

6          A297134     A297135     A297136

7          A297137     A297138     A297139

8          A297140     A297141     A297142

9          A297143     A297144     A297145

10         A297146     A297147     A297148

LINKS

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

EXAMPLE

Base-10 digits of 59898: 5,9,8,9,8, with pattern UDUD, so that 59898 is in the sequence.

MATHEMATICA

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;

b = 10; t = Table[a[n, b], {n, 1, 10*z}];

u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297146 *)

v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297147 *)

Complement[Range[z], Union[u, v]]  (* A297148 *)

CROSSREFS

Cf. A297147, A297148.

Sequence in context: A297272 A071589 A296713 * A267761 A324322 A083826

Adjacent sequences:  A297143 A297144 A297145 * A297147 A297148 A297149

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified January 24 19:12 EST 2021. Contains 340411 sequences. (Running on oeis4.)