A296864 Numbers whose base-4 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, 20, 21, 22, 23, 26, 27, 31, 32, 36, 37, 40, 41, 42, 43, 47, 48, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 73, 76, 77, 78, 80, 84, 85, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 104, 105

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 A296864-A296866 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-4 digits of 105 are 1, 2, 2, 1; here #(pits) = 0 and #(peaks) = 0, so 105 is in the sequence.

Mathematica

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

Crossrefs

Cf. A296882, A296712, A296865, A296866.

Sequence in context: A017909 A345201 A316530 * A124695 A005555 A128829

Adjacent sequences: A296861 A296862 A296863 * A296865 A296866 A296867

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved