

A297131


Numbers having an upfirst zigzag pattern in base 5; see Comments.


4



7, 8, 9, 13, 14, 19, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 65, 66, 67, 69, 70, 71, 72, 73, 95, 96, 97, 98, 176, 177, 178, 179, 180, 182, 183, 184, 190, 191, 192, 194, 195, 196, 197, 198, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 213, 214
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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 A297131A297133 partition the natural numbers. See the guide at A297146.


LINKS

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


EXAMPLE

Base5 digits of 4973: 1,2,4,3,4,3, with pattern UDUD, so that 4973 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. A297132, A297133.
Sequence in context: A170933 A297257 A296698 * A289740 A289760 A241289
Adjacent sequences: A297128 A297129 A297130 * A297132 A297133 A297134


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Jan 14 2018


STATUS

approved



