A296882 -id:A296882 - cp's OEIS frontend

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

Clark Kimberling, Jan 08 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 112 are 1,1,1,0,0,0,0; here #(pits) = 0 and #(peaks) = 0, so that 112 is in the sequence.

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

Cf. A296882, A296712, A296859, 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, 113)))) # Michael S. Branicky, May 11 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

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 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

A296861 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 12, 13, 14, 17, 18, 21, 22, 24, 25, 26, 27, 28, 29, 30, 33, 34, 36, 39, 40, 41, 44, 46, 47, 50, 51, 52, 53, 54, 55, 56, 57, 60, 61, 63, 66, 67, 68, 69, 70, 72, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 89, 90, 96, 97, 99, 102, 103

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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

			The base-3 digits of 103 are 1, 0, 2, 1, 1; here #(pits) = 1 and #(peaks) = 1, so 103 is in the sequence.

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

Cf. A296882, A296712, A296862, A296863.

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)

A296862 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

Original entry on oeis.org

10, 11, 19, 20, 23, 31, 32, 35, 37, 38, 58, 59, 62, 64, 65, 71, 73, 74, 77, 91, 92, 93, 94, 95, 98, 100, 101, 104, 105, 106, 107, 112, 113, 116, 118, 119, 154, 155, 158, 172, 173, 174, 175, 176, 179, 181, 182, 185, 186, 187, 188, 193, 194, 197, 199, 200, 208

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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

			The base-3 digits of 208 are 2, 1, 2, 0, 1; here #(pits) = 2 and #(peaks) = 1, so 208 is in the sequence.

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

Cf. A296882, A296712, A296861, A296863.

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)

A296863 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

Original entry on oeis.org

15, 16, 42, 43, 45, 48, 49, 84, 87, 88, 123, 124, 126, 129, 130, 135, 136, 137, 138, 141, 142, 144, 147, 148, 149, 150, 151, 165, 168, 169, 204, 205, 246, 249, 250, 252, 258, 259, 261, 264, 265, 327, 330, 331, 366, 367, 369, 372, 373, 378, 379, 380, 381, 384

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 A296861-A296863 partition the natural numbers. See the guides at A296882 and A296712.

			The base-3 digits of 384 are 1, 1, 2, 0, 2, 0; here #(pits) = 1 and #(peaks) = 2, so 384 is in the sequence.

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

Cf. A296882, A296712, A296861, A296862.

z = 200; b = 3;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296861 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296862 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296863 *)

A296864 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 20, 21, 22, 23, 26, 27, 31, 32, 36, 37, 40, 41, 42, 43, 47, 48, 52, 53, 56, 57, 58, 60, 61, 62, 63, 64, 65, 66, 67, 68, 72, 73, 76, 77, 78, 80, 84, 85, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 104, 105

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 105 are 1, 2, 2, 1; here #(pits) = 0 and #(peaks) = 0, so 105 is in the sequence.

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

Cf. A296882, A296712, A296865, A296866.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296865 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

Original entry on oeis.org

17, 18, 19, 33, 34, 35, 38, 39, 49, 50, 51, 54, 55, 59, 69, 70, 71, 74, 75, 79, 81, 82, 83, 133, 134, 135, 138, 139, 143, 145, 146, 147, 154, 155, 159, 161, 162, 163, 166, 167, 197, 198, 199, 202, 203, 207, 209, 210, 211, 218, 219, 223, 225, 226, 227, 230

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 230 are 3, 2, 1, 2; here #(pits) = 1 and #(peaks) = 0, so 230 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296864, A296866.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296866 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

Original entry on oeis.org

24, 25, 28, 29, 30, 44, 45, 46, 88, 89, 92, 93, 94, 96, 100, 101, 108, 109, 110, 112, 116, 117, 120, 121, 122, 172, 173, 174, 176, 180, 181, 184, 185, 186, 260, 264, 265, 268, 269, 270, 344, 345, 348, 349, 350, 352, 356, 357, 364, 365, 366, 368, 372, 373

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 A296864-A296866 partition the natural numbers. See the guides at A296882 and A296712.

			The base-4 digits of 373 are 1,1,3,1,1; here #(pits) = 0 and #(peaks) = 2, so 373 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296864, A296865.

z = 200; b = 4;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296864 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296865 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296866 *)

A296867 Numbers whose base-5 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

Original entry on oeis.org

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, 30, 31, 32, 33, 34, 37, 38, 39, 43, 44, 49, 50, 55, 56, 60, 61, 62, 63, 64, 68, 69, 74, 75, 80, 81, 85, 86, 87, 90, 91, 92, 93, 94, 99, 100, 105, 106, 110, 111, 112

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 A296867-A296869 partition the natural numbers. See the guides at A296882 and A296712.

			The base-5 digits of 112 are 4,2,2; here #(pits) = 0 and #(peaks) = 0, so 112 is in the sequence.

Clark Kimberling, Table of n, a(n) for n = 1..9999

Cf. A296882, A296712, A296868, A296869.

z = 200; b = 5;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296867 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]    (* A296868 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]    (* A296869 *)

cp's OEIS Frontend

A296858 Numbers whose base-2 digits 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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A296861 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296862 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

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A296863 Numbers whose base-3 digits d(m), d(m-1), ..., d(0) have #(pits) < #(peaks); see Comments.

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A296864 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296865 Numbers whose base-4 digits d(m), d(m-1), ..., d(0) have #(pits) > #(peaks); see Comments.

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