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A297129
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Numbers having a down-first zigzag pattern in base 4; see Comments.
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4
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4, 8, 9, 12, 13, 14, 17, 18, 19, 33, 34, 35, 36, 38, 39, 49, 50, 51, 52, 54, 55, 56, 57, 59, 68, 70, 71, 72, 73, 75, 76, 77, 78, 132, 134, 135, 136, 137, 139, 140, 141, 142, 145, 146, 147, 152, 153, 155, 156, 157, 158, 196, 198, 199, 200, 201, 203, 204, 205
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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 A297128-A297130 partition the natural numbers. See the guide at A297146.
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LINKS
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EXAMPLE
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Base-4 digits of 5000: 1,0,3,2,0,2,0, with pattern DUDUD, so that 5000 is in the sequence.
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MATHEMATICA
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a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 4; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297128 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297129 *)
Complement[Range[z], Union[u, v]] (* A297130 *)
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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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