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A297141
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Numbers having a down-first zigzag pattern in base 8; see Comments.
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4
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8, 16, 17, 24, 25, 26, 32, 33, 34, 35, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203
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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 A297140-A297142 partition the natural numbers. See the guide at A297146.
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LINKS
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EXAMPLE
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Base-8 digits of 4599: 1,0,7,6,7, with pattern DUDU, so that 4599 is in the sequence.
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MATHEMATICA
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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 *)
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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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