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A297143 Numbers having an up-first zigzag pattern in base 9; see Comments. 4
11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130 (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 A297143-A297145 partition the natural numbers.  See the guide at A297146.

LINKS

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

EXAMPLE

Base-9 digits of 10000: 1,4,6,4,1, with pattern UD, so that 10000 is in the sequence.

MATHEMATICA

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

b = 9; t = Table[a[n, b], {n, 1, 10*z}];

u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297143 *)

v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297144 *)

Complement[Range[z], Union[u, v]]  (* A297145 *)

CROSSREFS

Cf. A297144, A297145.

Sequence in context: A119247 A297269 A296710 * A138595 A192271 A214423

Adjacent sequences:  A297140 A297141 A297142 * A297144 A297145 A297146

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified July 5 19:02 EDT 2020. Contains 335473 sequences. (Running on oeis4.)