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A297125
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Numbers having a down-first zigzag pattern in base 3; see Comments.
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4
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3, 6, 7, 10, 11, 19, 20, 21, 23, 30, 32, 33, 34, 57, 59, 60, 61, 64, 65, 69, 70, 91, 92, 96, 97, 100, 101, 102, 104, 172, 173, 177, 178, 181, 182, 183, 185, 192, 194, 195, 196, 208, 209, 210, 212, 273, 275, 276, 277, 289, 290, 291, 293, 300, 302, 303, 304
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OFFSET
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1,1
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COMMENTS
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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 A297124..A297127 partition the natural numbers. See the guide at A297146.
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LINKS
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EXAMPLE
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Base-3 digits of 307: 1,0,2,1,0,1, with pattern DUDU, so that 307 is in the sequence.
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MATHEMATICA
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a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 3; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297124 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297125 *)
Complement[Range[z], Union[u, v]] (* A297126 *)
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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STATUS
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approved
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