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A297129 Numbers having a down-first zigzag pattern in base 4; see Comments. 4
4, 8, 9, 12, 13, 14, 17, 18, 19, 33, 34, 35, 36, 38, 39, 49, 50, 51, 52, 54, 55, 56, 57, 59, 68, 70, 71, 72, 73, 75, 76, 77, 78, 132, 134, 135, 136, 137, 139, 140, 141, 142, 145, 146, 147, 152, 153, 155, 156, 157, 158, 196, 198, 199, 200, 201, 203, 204, 205 (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 A297128-A297130 partition the natural numbers.  See the guide at A297146.

LINKS

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

EXAMPLE

Base-4 digits of 5000: 1,0,3,2,0,2,0, with pattern DUDUD, so that 5000 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. A297128, A297130.

Sequence in context: A266142 A297252 A296696 * A078137 A294574 A010453

Adjacent sequences:  A297126 A297127 A297128 * A297130 A297131 A297132

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 14 2018

STATUS

approved

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Last modified August 25 10:20 EDT 2019. Contains 326324 sequences. (Running on oeis4.)