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A296756
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Numbers whose base-15 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, 8, 9, 10, 11, 12, 13, 14, 16, 32, 48, 64, 80, 96, 112, 128, 144, 160, 176, 192, 208, 224, 226, 227, 228, 229, 230, 231, 232, 233, 234, 235, 236, 237, 238, 239, 241, 255, 256, 270, 271, 272, 285, 286, 287, 288, 300, 301, 302, 303, 304
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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 A296756-A296758 partition the natural numbers. See the guide at A296712.
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LINKS
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EXAMPLE
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The base-15 digits of 2^20 are 1, 5, 10, 10, 5, 1; here #(rises) = 2 and #(falls) = 2, so 2^20 is in the sequence.
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MATHEMATICA
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z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296757 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296758 *)
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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