A296860 Numbers k whose base-2 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

18, 34, 36, 50, 66, 68, 72, 73, 74, 82, 98, 100, 114, 130, 132, 136, 137, 138, 144, 145, 146, 147, 148, 162, 164, 194, 196, 200, 201, 202, 210, 226, 228, 242, 258, 260, 264, 265, 266, 272, 273, 274, 275, 276, 288, 289, 290, 291, 292, 293, 294, 295, 296, 297

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 297 are 1, 0, 0, 1, 0, 1, 0, 0, 1; here #(pits) = 1 and #(peaks) = 2, so 297 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, 298)))) # Michael S. Branicky, May 11 2021

Crossrefs

Cf. A296882, A296712, A296858, A296859.

Sequence in context: A188212 A093478 A214465 * A190150 A347369 A357439

Adjacent sequences: A296857 A296858 A296859 * A296861 A296862 A296863

Keyword

nonn,base,easy

Author

Clark Kimberling, Jan 09 2018

Status

approved