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A297131
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Numbers having an up-first zigzag pattern in base 5; see Comments.
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4
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7, 8, 9, 13, 14, 19, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 65, 66, 67, 69, 70, 71, 72, 73, 95, 96, 97, 98, 176, 177, 178, 179, 180, 182, 183, 184, 190, 191, 192, 194, 195, 196, 197, 198, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 213, 214
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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 A297131-A297133 partition the natural numbers. See the guide at A297146.
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LINKS
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EXAMPLE
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Base-5 digits of 4973: 1,2,4,3,4,3, with pattern UDUD, so that 4973 is in the sequence.
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MATHEMATICA
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a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 5; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &] (* A297131 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &] (* A297132 *)
Complement[Range[z], Union[u, v]] (* A297133 *)
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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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