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A297140 Numbers having an up-first zigzag pattern in base 8; see Comments. 4
10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122 (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 3575: 6, 7, 6, 7, with pattern UDU, so that 3575 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. A297141, A297142.

Sequence in context: A174397 A297266 A296707 * A173688 A008709 A008708

Adjacent sequences:  A297137 A297138 A297139 * A297141 A297142 A297143

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified January 20 13:55 EST 2022. Contains 350472 sequences. (Running on oeis4.)