

A296709


Numbers n whose base9 digits d(m), d(m1), ..., d(0) have #(rises) = #(falls); see Comments.


5



1, 2, 3, 4, 5, 6, 7, 8, 10, 20, 30, 40, 50, 60, 70, 80, 82, 83, 84, 85, 86, 87, 88, 89, 91, 99, 100, 108, 109, 110, 117, 118, 119, 120, 126, 127, 128, 129, 130, 135, 136, 137, 138, 139, 140, 144, 145, 146, 147, 148, 149, 150, 153, 154, 155, 156, 157, 158
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OFFSET

1,2


COMMENTS

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 A296709A296711 partition the natural numbers. See the guide at A296712.


LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000


EXAMPLE

The base9 digits of 158 are 1,8,5; here #(rises) = 1 and #(falls) = 1, so that 158 is in the sequence.


MATHEMATICA

z = 200; b = 9; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], 1] == Count[d[#], 1] &] (* A296709 *)
Select[Range [z], Count[d[#], 1] < Count[d[#], 1] &] (* A296710 *)
Select[Range [z], Count[d[#], 1] > Count[d[#], 1] &] (* A296711 *)


CROSSREFS

Cf. A296710, A296711, A296712.
Sequence in context: A297145 A048306 A043712 * A029955 A297268 A048320
Adjacent sequences: A296706 A296707 A296708 * A296710 A296711 A296712


KEYWORD

nonn,easy,base


AUTHOR

Clark Kimberling, Jan 08 2018


STATUS

approved



