A296712 -id:A296712 - cp's OEIS frontend

A296888 Numbers whose base-12 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 A296888-A296890 partition the natural numbers. See the guides at A296712 and A296882.

			The base-12 digits of 2030 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 2030 is in the sequence.

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

Cf. A296882, A296712, A296889, A296890.

z = 200; b = 12;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296888 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296889 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296890 *)

A296891 Numbers whose base-13 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, 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 A296891-A296894 partition the natural numbers. See the guides at A296712 and A296882.

			The base-13 digits of 2550 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 2550 is in the sequence.

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

Cf. A296882, A296712, A296892, A296893.

z = 200; b = 13;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296891 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296892 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296893 *)

A296900 Numbers whose base-16 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, 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 12 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 A296900-A296902 partition the natural numbers. See the guides at A296712 and A296882.

			The base-16 digits of 4626 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 4626 is in the sequence.

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

Cf. A296882, A296712, A296901, A296902.

z = 200; b = 16;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296900 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296901 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296902 *)

A296903 Numbers whose base-20 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, 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 12 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 A296903-A296905 partition the natural numbers.

a(n) = n for n = 1..400, but not for n = 401. See the guides at A296712 and A296882.

			The base-20 digits of 8822 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 8822 is in the sequence.

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

Cf. A296882, A296712, A296904, A296905.

z = 200; b = 20;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296903 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296904 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296905 *)

A296906 Numbers whose base-60 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, 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 12 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 A296906..A296908 partition the natural numbers.

a(n) = n for n = 1..3600, but not for n = 3601. See the guides at A296712 and A296882.

			The base-60 digits of 223262 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 223262 is in the sequence.

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

Cf. A296882, A296712, A296907, A296908.

z = 200; b = 60;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296906 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296907 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296908 *)

A296691 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 4, 8, 10, 11, 13, 15, 16, 19, 20, 23, 26, 28, 29, 31, 35, 37, 38, 40, 42, 43, 45, 49, 51, 52, 55, 56, 58, 62, 68, 71, 73, 74, 77, 80, 82, 83, 85, 89, 91, 92, 94, 96, 97, 100, 101, 104, 107, 109, 110, 112, 116, 118, 119, 121, 123, 124, 126, 130, 132

Offset: 1

Clark Kimberling, Dec 19 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296691-A296693 partition the natural numbers. See the guide at A296712.

			The base-3 digits of 132 are 1,1,2,2,0; here #(rises) = #(falls) = 1, so 132 is in the sequence.

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

Cf. A296692, A296693, A296712.

z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)

A296692 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

5, 14, 17, 32, 41, 44, 46, 47, 50, 53, 59, 86, 95, 98, 113, 122, 125, 127, 128, 131, 134, 136, 137, 139, 140, 143, 149, 152, 154, 155, 158, 161, 167, 176, 179, 221, 248, 257, 260, 275, 284, 287, 289, 290, 293, 296, 302, 329, 338, 341, 356, 365, 368, 370, 371

Offset: 1

Clark Kimberling, Dec 19 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296691-A296693 partition the natural numbers. See the guide at A296712.

			The base-3 digits of 371 are 1,1,1,2,0,2; here #(rises) = 2 and #(falls) = 1, so 371 is in the sequence.

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

Cf. A296691, A296693, A296712.

z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)

A296693 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

3, 6, 7, 9, 12, 18, 21, 22, 24, 25, 27, 30, 33, 34, 36, 39, 48, 54, 57, 60, 61, 63, 64, 65, 66, 67, 69, 70, 72, 75, 76, 78, 79, 81, 84, 87, 88, 90, 93, 99, 102, 103, 105, 106, 108, 111, 114, 115, 117, 120, 129, 144, 147, 156, 162, 165, 168, 169, 171, 174

Offset: 1

Clark Kimberling, Dec 19 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296691-A296693 partition the natural numbers. See the guide at A296712.

			The base-3 digits of 174 are 2,0,1,1,0; here #(rises) = 1 and #(falls) = 2, so 174 is in the sequence.

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

Cf. A296691, A296692, A296712.

z = 200; b = 3; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296691 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296692 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296693 *)
rltfQ[n_]:=Module[{d=Differences[IntegerDigits[n,3]]},Count[d,?(#>0&)]<Count[d,?(#<0&)]]; Select[Range[200],rltfQ] (* Harvey P. Dale, Sep 25 2019 *)

A296694 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 3, 5, 10, 15, 17, 18, 19, 21, 24, 25, 28, 29, 30, 33, 34, 35, 38, 39, 42, 44, 45, 46, 49, 50, 51, 54, 55, 59, 63, 65, 66, 67, 69, 74, 79, 81, 82, 83, 85, 88, 89, 92, 93, 94, 96, 101, 104, 105, 112, 117, 122, 124, 125, 126, 129, 130, 131, 133, 138, 143

Offset: 1

Clark Kimberling, Dec 21 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296694-A296696 partition the natural numbers. See the guide at A296712.

			The base-4 digits of 143 are 2,0,3,3; here #(rises) = 1 and #(falls) = 1, so 143 is in the sequence.

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

Cf. A296695, A296696, A296700, A296712.

z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296696 *)

A296695 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

6, 7, 11, 22, 23, 26, 27, 31, 43, 47, 70, 71, 75, 86, 87, 90, 91, 95, 97, 98, 99, 102, 103, 106, 107, 108, 109, 110, 111, 113, 114, 115, 118, 119, 123, 127, 134, 135, 139, 155, 171, 175, 177, 178, 179, 182, 183, 187, 191, 198, 199, 203, 219, 262, 263, 267

Offset: 1

Clark Kimberling, Dec 21 2017

A rise is an index i such that d(i) < d(i+1); a fall is an index i such that d(i) > d(i+1). The sequences A296694-A296696 partition the natural numbers. See the guide at A296712.

			The base-4 digits of 267 are 1,0,0,2,3; here #(rises) = 2 and #(falls) = 1, so 267 is in the sequence.

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

Cf. A296694, A296696, A296712.

z = 200; b = 4; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296694 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296695 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296696 *)

cp's OEIS Frontend

A296888 Numbers whose base-12 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296891 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296900 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296903 Numbers whose base-20 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296906 Numbers whose base-60 digits d(m), d(m-1), ..., d(0) have #(pits) = #(peaks); see Comments.

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A296691 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

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A296692 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.

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A296693 Numbers whose base-3 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

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