A296896 - OEIS

%I #7 Jan 21 2023 18:06:09

%S 224,225,238,239,240,252,253,254,255,266,267,268,269,270,280,281,282,

%T 283,284,285,294,295,296,297,298,299,300,308,309,310,311,312,313,314,

%U 315,322,323,324,325,326,327,328,329,330,336,337,338,339,340,341,342,343

%N Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

%C A pit is an index i such that d(i-1) > d(i) < d(i+1); a peak is an index i such that d(i-1) < d(i) > d(i+1). The sequences A296894-A296896 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296896/b296896.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-14 digits of 44129 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 44129 is in the sequence.

%t z = 200; b = 14;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296894 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296895 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296896 *)

%Y Cf. A296882, A296712, A296894, A296895.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018