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A297131 Numbers having an up-first zigzag pattern in base 5; see Comments. 4
7, 8, 9, 13, 14, 19, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 65, 66, 67, 69, 70, 71, 72, 73, 95, 96, 97, 98, 176, 177, 178, 179, 180, 182, 183, 184, 190, 191, 192, 194, 195, 196, 197, 198, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 213, 214 (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 A297131-A297133 partition the natural numbers.  See the guide at A297146.

LINKS

Table of n, a(n) for n=1..58.

EXAMPLE

Base-5 digits of 4973: 1,2,4,3,4,3, with pattern UDUD, so that 4973 is in the sequence.

MATHEMATICA

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

b = 5; t = Table[a[n, b], {n, 1, 10*z}];

u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297131 *)

v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297132 *)

Complement[Range[z], Union[u, v]]  (* A297133 *)

CROSSREFS

Cf. A297132, A297133.

Sequence in context: A170933 A297257 A296698 * A289740 A289760 A241289

Adjacent sequences:  A297128 A297129 A297130 * A297132 A297133 A297134

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 14 2018

STATUS

approved

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)