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A297144 Numbers having a down-first zigzag pattern in base 9; see Comments. 4
9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 244 (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

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

Base-9 digits of 7280: 1,0,8,7,8, with pattern DUDU, so that 7280 is in the sequence.

MAPLE

filter:= proc(n)  local L;

L:= convert(n, base, 9);

not has(L[2..-1]-L[1..-2], 0) and L[-1]>L[-2]

end proc:

select(filter, [$9..1000]); # Robert Israel, Dec 06 2018

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. A297143, A297145.

Sequence in context: A060993 A297267 A296711 * A107977 A257226 A092457

Adjacent sequences:  A297141 A297142 A297143 * A297145 A297146 A297147

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 15 2018

STATUS

approved

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Last modified June 22 21:29 EDT 2021. Contains 345393 sequences. (Running on oeis4.)