

A297132


Numbers having a downfirst 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
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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..59.


EXAMPLE

Base5 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



