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 A296706 Numbers n whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments. 4

%I

%S 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,

%T 89,90,96,97,98,99,104,105,106,107,108,112,113,114,115,116,117,120,

%U 121,122,123,124,125,126,129,130,131,132,133,134,135,138,139,140

%N Numbers n whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

%C 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.

%H Clark Kimberling, <a href="/A296706/b296706.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-8 digits of 140 are 2,1,4; here #(rises) = 1 and #(falls) = 1, so that 140 is in the sequence.

%t z = 200; b = 8; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296706 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296707 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296708 *)

%Y Cf. A296707, A296708, A296712.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Jan 08 2018

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Last modified January 27 17:58 EST 2020. Contains 331296 sequences. (Running on oeis4.)