A296902 - OEIS

%I #8 Jan 21 2023 02:23:16

%S 288,289,304,305,306,320,321,322,323,336,337,338,339,340,352,353,354,

%T 355,356,357,368,369,370,371,372,373,374,384,385,386,387,388,389,390,

%U 391,400,401,402,403,404,405,406,407,408,416,417,418,419,420,421,422,423

%N Numbers whose base-16 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 A296900-A296902 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296902/b296902.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-16 digits of 74017 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 74017 is in the sequence.

%t z = 200; b = 16;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296900 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296901 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296902 *)

%Y Cf. A296882, A296712, A296900, A296901.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018