A296858 -id:A296858 - cp's OEIS frontend

A296882 Numbers whose base-10 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, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67

Offset: 1

Clark Kimberling, Jan 10 2018

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 A296882-A296883 partition the natural numbers. See the guides at A296712.  We have a(n) = A000027(n) for n=1..100 but not n=101.
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Guide to related sequences:
Base    #(pits) = #(peaks)  #(pits) > #(peaks)    #(pits) < #(peaks)
          A296858             A296859               A296860
          A296861             A296862               A296863
          A296864             A296865               A296866
          A296867             A296868               A296869
          A296870             A296871               A296872
          A296873             A296874               A296875
          A296876             A296877               A296878
          A296879             A296880               A296881
         A296882             A296883               A296884
         A296885             A296886               A296887
         A296888             A296889               A296890
         A296891             A296892               A296893
         A296894             A296895               A296896
         A296897             A296898               A296899
         A296900             A296901               A296902
         A296903             A296904               A296905
         A296906             A296907               A296908

			The base-10 digits of 1212 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 1212 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A296882, A296712, A296883, A296884.

z = 200; b = 10;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296882 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296883 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296884 *)

Overview table corrected by Georg Fischer, Aug 24 2021

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

Original entry on oeis.org

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

Clark Kimberling, Jan 09 2018

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.

			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.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A296882, A296712, A296858, A296860.

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 *)

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

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

Original entry on oeis.org

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

Clark Kimberling, Jan 09 2018

			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.

Clark Kimberling, Table of n, a(n) for n = 1..10000

Cf. A296882, A296712, A296858, A296859.

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 *)

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

cp's OEIS Frontend

A296882 Numbers whose base-10 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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

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

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Python