A296890 - OEIS

%I #7 Jan 21 2023 18:16:56

%S 168,169,180,181,182,192,193,194,195,204,205,206,207,208,216,217,218,

%T 219,220,221,228,229,230,231,232,233,234,240,241,242,243,244,245,246,

%U 247,252,253,254,255,256,257,258,259,260,264,265,266,267,268,269,270,271

%N Numbers whose base-12 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 A296888-A296890 partition the natural numbers. See the guides at A296712 and A296882.

%H Clark Kimberling, <a href="/A296890/b296890.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-12 digits of 24361 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 24361 is in the sequence.

%t z = 200; b = 12;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296888 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296889 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296890 *)

%Y Cf. A296882, A296712, A296888, A296889.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 10 2018