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A296706
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Numbers n whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.
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4
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1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 65, 66, 67, 68, 69, 70, 71, 73, 80, 81, 88, 89, 90, 96, 97, 98, 99, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140
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OFFSET
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1,2
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COMMENTS
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A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296706-A296707 partition the natural numbers. See the guide at A296712.
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LINKS
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Clark Kimberling, Table of n, a(n) for n = 1..10000
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EXAMPLE
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The base-8 digits of 140 are 2,1,4; here #(rises) = 1 and #(falls) = 1, so that 140 is in the sequence.
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MATHEMATICA
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z = 200; b = 8; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296706 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296707 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296708 *)
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CROSSREFS
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Cf. A296707, A296708, A296712.
Sequence in context: A044819 A048305 A043711 * A029803 A297265 A048319
Adjacent sequences: A296703 A296704 A296705 * A296707 A296708 A296709
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KEYWORD
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nonn,easy,base
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AUTHOR
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Clark Kimberling, Jan 08 2018
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STATUS
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approved
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