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A297135 Numbers having a down-first zigzag pattern in base 6; see Comments. 4
6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 123, 124, 125, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159 (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 A297134-A297136 partition the natural numbers.  See the guide at A297146.

LINKS

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

EXAMPLE

Base-6 digits of 4529: 3,2,5,4,5, with pattern DUDU, so that 4529 is in the sequence.

MATHEMATICA

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

b = 6; t = Table[a[n, b], {n, 1, 10*z}];

u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *)

v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *)

Complement[Range[z], Union[u, v]]  (* A297136 *)

CROSSREFS

Cf. A297134, A297136.

Sequence in context: A337480 A297258 A296702 * A004758 A055051 A338054

Adjacent sequences:  A297132 A297133 A297134 * A297136 A297137 A297138

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 14 2018

STATUS

approved

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Last modified November 27 09:19 EST 2021. Contains 349365 sequences. (Running on oeis4.)