A296872 - OEIS

%I #11 Jan 22 2023 18:58:45

%S 48,49,54,55,56,60,61,62,63,66,67,68,69,70,90,91,92,96,97,98,99,102,

%T 103,104,105,106,132,133,134,135,138,139,140,141,142,174,175,176,177,

%U 178,264,265,270,271,272,276,277,278,279,282,283,284,285,286,288,294

%N Numbers whose base-6 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 A296870-A296872 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296872/b296872.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-6 digits of 294 are 1,2,1,0; here #(pits) = 0 and #(peaks) = 1, so 294 is in the sequence.

%t z = 200; b = 6;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296870 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296871 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296872 *)

%Y Cf. A296882, A296712, A296870, A296871.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018