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A296860

Numbers k whose base-2 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

18, 34, 36, 50, 66, 68, 72, 73, 74, 82, 98, 100, 114, 130, 132, 136, 137, 138, 144, 145, 146, 147, 148, 162, 164, 194, 196, 200, 201, 202, 210, 226, 228, 242, 258, 260, 264, 265, 266, 272, 273, 274, 275, 276, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297

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OFFSET

1,1

COMMENTS

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 A296858-A296860 partition the natural numbers. See the guides at A296882 and A296712.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..10000

EXAMPLE

The base-2 digits of 297 are 1, 0, 0, 1, 0, 1, 0, 0, 1; here #(pits) = 1 and #(peaks) = 2, so 297 is in the sequence.

MATHEMATICA

z = 200; b = 2;

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

Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296858 *)

Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296859 *)

Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296860 *)

PROG

(Python)