

A297143


Numbers having an upfirst zigzag pattern in base 9; see Comments.


4



11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,1


COMMENTS

A number n having baseb digits d(m), d(m1),..., 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 "upfirst zigzag pattern in base b"; in the latter, a "downfirst 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 upfirst zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a downfirst pattern. The sequences A297143A297145 partition the natural numbers. See the guide at A297146.


LINKS

Table of n, a(n) for n=1..57.


EXAMPLE

Base9 digits of 10000: 1,4,6,4,1, with pattern UD, so that 10000 is in the sequence.


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. A297144, A297145.
Sequence in context: A119247 A297269 A296710 * A138595 A192271 A214423
Adjacent sequences: A297140 A297141 A297142 * A297144 A297145 A297146


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



