A296867 Numbers whose base-5 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, 30, 31, 32, 33, 34, 37, 38, 39, 43, 44, 49, 50, 55, 56, 60, 61, 62, 63, 64, 68, 69, 74, 75, 80, 81, 85, 86, 87, 90, 91, 92, 93, 94, 99, 100, 105, 106, 110, 111, 112

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 A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.

Links

Clark Kimberling, Table of n, a(n) for n = 1..9999

Example

The base-5 digits of 112 are 4,2,2; here #(pits) = 0 and #(peaks) = 0, so 112 is in the sequence.

Mathematica

z = 200; b = 5;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296867 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]    (* A296868 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]    (* A296869 *)

Crossrefs

Cf. A296882, A296712, A296868, A296869.

Sequence in context: A032521 A246102 A243903 * A228144 A236841 A236850

Adjacent sequences: A296864 A296865 A296866 * A296868 A296869 A296870

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved