A296893 - OEIS

%I #7 Jan 21 2023 18:12:59

%S 195,196,208,209,210,221,222,223,224,234,235,236,237,238,247,248,249,

%T 250,251,252,260,261,262,263,264,265,266,273,274,275,276,277,278,279,

%U 280,286,287,288,289,290,291,292,293,294,299,300,301,302,303,304,305,306

%N Numbers whose base-13 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 A296891-A296894 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296893/b296893.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-13 digits of 33151 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 33151 is in the sequence.

%t z = 200; b = 13;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296891 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296892 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296893 *)

%Y Cf. A296882, A296712, A296891, A296892.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018