A296858 Numbers whose base-2 digits have #(pits) = #(peaks); see Comments.

1, 2, 3, 4, 6, 7, 8, 9, 10, 12, 14, 15, 16, 17, 19, 20, 24, 25, 26, 28, 30, 31, 32, 33, 35, 37, 38, 39, 40, 41, 42, 48, 49, 51, 52, 56, 57, 58, 60, 62, 63, 64, 65, 67, 69, 70, 71, 75, 76, 78, 79, 80, 81, 83, 84, 96, 97, 99, 101, 102, 103, 104, 105, 106, 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 A296858-A296860 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-2 digits of 112 are 1,1,1,0,0,0,0; here #(pits) = 0 and #(peaks) = 0, so that 112 is in the sequence.

Mathematica

z = 200; b = 2;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]   (* A296858 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]    (* A296859 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]    (* A296860 *)

Prog

(Python)
def cwo(subs, s): # count with overlaps allowed
  c = i = 0
  while i != -1:
    i = s.find(subs, i)
    if i != -1: c += 1; i += 1
  return c
def ok(n): b = bin(n)[2:]; return cwo('101', b) == cwo('010', b)
print(list(filter(ok, range(1, 113)))) # Michael S. Branicky, May 11 2021

Crossrefs

Cf. A296882, A296712, A296859, A296860.

Sequence in context: A275804 A141825 A238369 * A296241 A070932 A161577

Adjacent sequences: A296855 A296856 A296857 * A296859 A296860 A296861

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 08 2018

Status

approved