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A297135
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Numbers having a down-first zigzag pattern in base 6; see Comments.
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4
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6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 123, 124, 125, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159
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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 A297134-A297136 partition the natural numbers. See the guide at A297146.
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LINKS
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EXAMPLE
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Base-6 digits of 4529: 3,2,5,4,5, with pattern DUDU, so that 4529 is in the sequence.
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MATHEMATICA
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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 *)
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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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