

A297140


Numbers having an upfirst zigzag pattern in base 8; see Comments.


4



10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122
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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 A297140A297142 partition the natural numbers. See the guide at A297146.


LINKS

Table of n, a(n) for n=1..59.


EXAMPLE

Base8 digits of 3575: 6, 7, 6, 7, with pattern UDU, so that 3575 is in the sequence.


MATHEMATICA

a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 8; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297140 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297141 *)
Complement[Range[z], Union[u, v]] (* A297142 *)


CROSSREFS

Cf. A297141, A297142.
Sequence in context: A174397 A297266 A296707 * A173688 A008709 A008708
Adjacent sequences: A297137 A297138 A297139 * A297141 A297142 A297143


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Jan 15 2018


STATUS

approved



