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Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.
4

%I #8 Jan 21 2023 02:23:20

%S 257,258,259,260,261,262,263,264,265,266,267,268,269,270,271,513,514,

%T 515,516,517,518,519,520,521,522,523,524,525,526,527,530,531,532,533,

%U 534,535,536,537,538,539,540,541,542,543,769,770,771,772,773,774,775,776

%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="/A296901/b296901.txt">Table of n, a(n) for n = 1..10000</a>

%e The base-16 digits of 135698 are 2,1,2,1,2; here #(pits) = 2 and #(peaks) = 1, so 135698 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, A296902.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 12 2018