A296870 Numbers whose base-6 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 42, 43, 44, 45, 46, 47, 50, 51, 52, 53, 57, 58, 59, 64, 65, 71, 72, 78, 79, 84, 85, 86, 87, 88, 89, 93, 94, 95, 100, 101

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 A296870-A296872 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-6 digits of 101 are 2,4,5; here #(pits) = 0 and #(peaks) = 0, so 101 is in the sequence.

Mathematica

z = 200; b = 6;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296870 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296871 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296872 *)

Crossrefs

Cf. A296882, A296712, A296871, A296872.

Sequence in context: A212554 A178772 A367141 * A085735 A269393 A269394

Adjacent sequences: A296867 A296868 A296869 * A296871 A296872 A296873

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved