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A296861

Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 17, 18, 21, 22, 24, 25, 26, 27, 28, 29, 30, 33, 34, 36, 39, 40, 41, 44, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 63, 66, 67, 68, 69, 70, 72, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 89, 90, 96, 97, 99, 102, 103

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OFFSET

1,2

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 A296861-A296863 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-3 digits of 103 are 1, 0, 2, 1, 1; here #(pits) = 1 and #(peaks) = 1, so 103 is in the sequence.

MATHEMATICA

z = 200; b = 3;

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

Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296861 *)

Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296862 *)

Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296863 *)

CROSSREFS

Cf. A296882, A296712, A296862, A296863.