A296866 - OEIS

%I #7 Jan 22 2023 20:51:02

%S 24,25,28,29,30,44,45,46,88,89,92,93,94,96,100,101,108,109,110,112,

%T 116,117,120,121,122,172,173,174,176,180,181,184,185,186,260,264,265,

%U 268,269,270,344,345,348,349,350,352,356,357,364,365,366,368,372,373

%N Numbers whose base-4 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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296866/b296866.txt">Table of n, a(n) for n = 1..9999</a>

%e The base-4 digits of 373 are 1,1,3,1,1; here #(pits) = 0 and #(peaks) = 2, so 373 is in the sequence.

%t z = 200; b = 4;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

%Y Cf. A296882, A296712, A296864, A296865.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018