A296890 - OEIS

A296890

Numbers whose base-12 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

168, 169, 180, 181, 182, 192, 193, 194, 195, 204, 205, 206, 207, 208, 216, 217, 218, 219, 220, 221, 228, 229, 230, 231, 232, 233, 234, 240, 241, 242, 243, 244, 245, 246, 247, 252, 253, 254, 255, 256, 257, 258, 259, 260, 264, 265, 266, 267, 268, 269, 270, 271

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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 A296888-A296890 partition the natural numbers. See the guides at A296712 and A296882.

LINKS

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

EXAMPLE

The base-12 digits of 24361 are 1,2,1,2,1; here #(pits) = 1 and #(peaks) = 2, so 24361 is in the sequence.

MATHEMATICA

z = 200; b = 12;

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

Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &] (* A296888 *)

Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &] (* A296889 *)

Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &] (* A296890 *)

CROSSREFS

Cf. A296882, A296712, A296888, A296889.