Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%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