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A297132 Numbers having a down-first zigzag pattern in base 5; see Comments. 4
5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 26, 27, 28, 29, 51, 52, 53, 54, 55, 57, 58, 59, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 88, 89, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 119, 130, 132, 133, 134, 135, 136, 138, 139, 140 (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..59.

EXAMPLE

Base-5 digits of 3723: 1,0,4,3,4,3, with pattern DUDUD, so that 3723 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. A297131, A297133.

Sequence in context: A140507 A297255 A296699 * A136823 A275200 A225838

Adjacent sequences:  A297129 A297130 A297131 * A297133 A297134 A297135

KEYWORD

nonn,easy,base

AUTHOR

Clark Kimberling, Jan 14 2018

STATUS

approved

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Last modified October 16 20:36 EDT 2021. Contains 348047 sequences. (Running on oeis4.)