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 A296753 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments. 6

%I #9 Jan 27 2023 19:26:08

%S 1,2,3,4,5,6,7,8,9,10,11,12,13,15,30,45,60,75,90,105,120,135,150,165,

%T 180,195,197,198,199,200,201,202,203,204,205,206,207,208,209,211,224,

%U 225,238,239,240,252,253,254,255,266,267,268,269,270,280,281,282

%N Numbers whose base-14 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 A296753-A296755 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296753/b296753.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-14 digits of 1000000 are 2,8,6,2,12; here #(rises) = 2 and #(falls) = 2, so 1000000 is in the sequence.

%t z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296754 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296755 *)

%t Select[Range[300],Total[Sign[Differences[IntegerDigits[#,14]]]]==0&] (* _Harvey P. Dale_, Sep 20 2022 *)

%Y Cf. A296754, A296755, A296712.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_, Jan 08 2018

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Last modified November 28 19:28 EST 2023. Contains 367419 sequences. (Running on oeis4.)