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A297134
Numbers having an up-first zigzag pattern in base 6; see Comments.
4
8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 174, 175, 176, 177, 178
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 A297134-A297136 partition the natural numbers. See the guide at A297146.
EXAMPLE
Base-6 digits of 5000: 3,5,0,5,2, with pattern UDUD, so that 5000 is in the sequence.
MATHEMATICA
a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 6; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297134 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297135 *)
Complement[Range[z], Union[u, v]] (* A297136 *)
CROSSREFS
Sequence in context: A247631 A297260 A296701 * A247455 A280290 A138581
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Jan 14 2018
STATUS
approved