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A296703 Numbers n whose base-7 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments. 4

%I

%S 1,2,3,4,5,6,8,16,24,32,40,48,50,51,52,53,54,55,57,63,64,70,71,72,77,

%T 78,79,80,84,85,86,87,88,91,92,93,94,95,96,99,100,101,102,103,104,107,

%U 108,109,110,111,114,119,120,121,126,127,128,129,133,134,135

%N Numbers n whose base-7 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 A296703-A296705 partition the natural numbers. See the guide at A296712.

%H Clark Kimberling, <a href="/A296703/b296703.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-7 digits of 135 are 2,5,2; here #(rises) = 1 and #(falls) = 1, so that 135 is in the sequence.

%t z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];

%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)

%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296704 *)

%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296705 *)

%Y Cf. A296704, A296705, A296712.

%K nonn,easy,base

%O 1,2

%A _Clark Kimberling_, Jan 07 2018

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Last modified December 13 06:26 EST 2019. Contains 329968 sequences. (Running on oeis4.)