A296873 Numbers whose base-7 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, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 73, 74, 75, 76, 81, 82

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 A296873-A296875 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-7 digits of 82 are 1,4,5; here #(pits) = 0 and #(peaks) = 0, so 82 is in the sequence.

Mathematica

z = 200; b = 7;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296873 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296874 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296875 *)

Crossrefs

Cf. A296882, A296712, A296874, A296875.

Sequence in context: A272554 A179797 A268200 * A044923 A180925 A272302

Adjacent sequences: A296870 A296871 A296872 * A296874 A296875 A296876

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved