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A297141 Numbers having a down-first zigzag pattern in base 8; see Comments. 4
8, 16, 17, 24, 25, 26, 32, 33, 34, 35, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203 (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 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 4599: 1,0,7,6,7, with pattern DUDU, so that 4599 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. A297140, A297142.

Sequence in context: A091251 A297264 A296708 * A004779 A247061 A180860

Adjacent sequences:  A297138 A297139 A297140 * A297142 A297143 A297144

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified January 21 09:14 EST 2022. Contains 350475 sequences. (Running on oeis4.)