%I #7 Jan 21 2023 18:06:25

%S 80,81,88,89,90,96,97,98,99,104,105,106,107,108,112,113,114,115,116,

%T 117,120,121,122,123,124,125,126,152,153,154,160,161,162,163,168,169,

%U 170,171,172,176,177,178,179,180,181,184,185,186,187,188,189,190,224

%N Numbers whose base-8 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 A296876-A296878 partition the natural numbers. See the guides at A296882 and A296712.

%H Clark Kimberling, <a href="/A296878/b296878.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-8 digits of 224 are 3,4,0; here #(pits) = 0 and #(peaks) = 1, so 224 is in the sequence.

%t z = 200; b = 8;

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

%t Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296876 *)

%t Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296877 *)

%t Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296878 *)

%Y Cf. A296882, A296712, A296876, A296877.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 09 2018