A296859 Numbers whose base-2 digits have #(pits) > #(peaks); see Comments.

5, 11, 13, 21, 22, 23, 27, 29, 43, 44, 45, 46, 47, 53, 54, 55, 59, 61, 77, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 107, 108, 109, 110, 111, 117, 118, 119, 123, 125, 141, 155, 157, 171, 172, 173, 174, 175, 176, 177, 179, 180, 181, 182, 183, 184, 185, 186

Offset

1,1

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 186 are 1,0,1,1,1,0,1,0; here #(pits) = 2 and #(peaks) = 1, so 186 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, 187)))) # Michael S. Branicky, May 11 2021

Crossrefs

Cf. A296882, A296712, A296858, A296860.

Sequence in context: A157750 A359501 A045449 * A313992 A346304 A190620

Adjacent sequences: A296856 A296857 A296858 * A296860 A296861 A296862

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved