|
%I #9 Jan 27 2023 19:27:13
%S 1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,17,34,51,68,85,102,119,136,153,
%T 170,187,204,221,238,255,257,258,259,260,261,262,263,264,265,266,267,
%U 268,269,270,271,273,288,289,304,305,306,320,321,322,323,336,337
%N Numbers whose base-16 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 A296759-A296761 partition the natural numbers. See the guide at A296712.
%H Clark Kimberling, <a href="/A296759/b296759.txt">Table of n, a(n) for n = 1..10000</a>
%e The base-16 digits of 2^20 + 1 are 1, 0, 0, 0, 0, 1; here #(rises) = 1 and #(falls) = 1, so 2^20 + 1 is in the sequence.
%t z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
%t Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
%t Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &] (* A296760 *)
%t Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &] (* A296761 *)
%t Select[Range[400],Total[Sign[Differences[IntegerDigits[#,16]]]]==0&] (* _Harvey P. Dale_, Aug 11 2021 *)
%Y Cf. A296760, A296761, A296712.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Jan 08 2018
|
