A296712 -id:A296712 - cp's OEIS frontend

A296751 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 43, 44, 45, 46, 47, 48, 49, 50, 51, 57, 58, 59, 60, 61, 62, 63, 64, 71, 72, 73, 74, 75, 76, 77, 85, 86, 87, 88, 89, 90, 99, 100, 101, 102, 103, 113, 114, 115, 116, 127, 128

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296751-A296753 partition the natural numbers. See the guide at A296712.

			The base-13 digits of 1000 are 5,11,12; here #(rises) = 2 and #(falls) = 0, so 1000 is in the sequence.

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

Cf. A296750, A296752, A296712.

z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)

A296752 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

13, 26, 27, 39, 40, 41, 52, 53, 54, 55, 65, 66, 67, 68, 69, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 104, 105, 106, 107, 108, 109, 110, 111, 117, 118, 119, 120, 121, 122, 123, 124, 125, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 143, 144

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296751-A296753 partition the natural numbers. See the guide at A296712.

			The base-13 digits of 914 are 5,5,4; here #(rises) = 0 and #(falls) = 1, so 914 is in the sequence.

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

Cf. A296750, A296751, A296712.

z = 200; b = 13; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296750 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296751 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296752 *)

A296754 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 61, 62, 63, 64, 65, 66, 67, 68, 69, 76, 77, 78, 79, 80, 81, 82, 83, 91, 92, 93, 94, 95, 96, 97, 106, 107, 108, 109, 110, 111

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296753-A296755 partition the natural numbers. See the guide at A296712.

			The base-14 digits of 10000000 are 1,12,0,6,0,8; here #(rises) = 3 and #(falls) = 2, so 10000000 is in the sequence.

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

Cf. A296753, A296755, A296712.

z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296754 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296755 *)

A296755 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

14, 28, 29, 42, 43, 44, 56, 57, 58, 59, 70, 71, 72, 73, 74, 84, 85, 86, 87, 88, 89, 98, 99, 100, 101, 102, 103, 104, 112, 113, 114, 115, 116, 117, 118, 119, 126, 127, 128, 129, 130, 131, 132, 133, 134, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 154

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296753-A296755 partition the natural numbers. See the guide at A296712.

			The base-14 digits of 10^9 are 9, 6, 11, 4, 11, 6, 11, 6; here #(rises) = 3 and #(falls) = 4, so 10^9 is in the sequence.

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

Cf. A296753, A296754, A296712.

z = 200; b = 14; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296753 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296754 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296755 *)

A296757 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 81, 82, 83, 84, 85, 86, 87, 88, 89, 97, 98, 99, 100, 101, 102, 103, 104

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296756-A296758 partition the natural numbers. See the guide at A296712.

			The base-15 digits of 2^20 + 6 are 1, 5, 10, 10, 5, 7; here #(rises) = 3 and #(falls) = 1, so 2^20 + 6 is in the sequence.

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

Cf. A296756, A296758, A296712.

z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296757 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296758 *)

A296758 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

15, 30, 31, 45, 46, 47, 60, 61, 62, 63, 75, 76, 77, 78, 79, 90, 91, 92, 93, 94, 95, 105, 106, 107, 108, 109, 110, 111, 120, 121, 122, 123, 124, 125, 126, 127, 135, 136, 137, 138, 139, 140, 141, 142, 143, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 165

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296756-A296758 partition the natural numbers. See the guide at A296712.

			The base-15 digits of 15^5 are 1, 0, 0, 0, 0, 0; here #(rises) = 0 and #(falls) = 1, so 15^5 is in the sequence.

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

Cf. A296756, A296757, A296712.

z = 200; b = 15; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296756 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296757 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296758 *)

A296760 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 103, 104, 105, 106

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296759-A296761 partition the natural numbers. See the guide at A296712.

			The base-16 digits of 106 are 6,10; here #(rises) = 1 and #(falls) = 0, so 106 is in the sequence.

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

Cf. A296759, A296761, A296712.

z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296760 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296761 *)
rgf16Q[n_]:=Total[Sign[#]&/@Differences[IntegerDigits[n,16]]]>0;Select[Range[150],rgf16Q] (* Harvey P. Dale, Nov 26 2023 *)

A296761 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

16, 32, 33, 48, 49, 50, 64, 65, 66, 67, 80, 81, 82, 83, 84, 96, 97, 98, 99, 100, 101, 112, 113, 114, 115, 116, 117, 118, 128, 129, 130, 131, 132, 133, 134, 135, 144, 145, 146, 147, 148, 149, 150, 151, 152, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169

Offset: 1

Clark Kimberling, Jan 08 2018

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 A296759-A296761 partition the natural numbers. See the guide at A296712.

			The base-16 digits of 32 are 2,0; here #(rises) = 0 and #(falls) = 2, so 32 is in the sequence.

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

Cf. A296759, A296760, A296712.

z = 200; b = 16; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296759 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296760 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296761 *)

A296879 Numbers whose base-9 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 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 A296879-A296881 partition the natural numbers. See the guides at A296882 and A296712.

			The base-9 digits of 67 are 7,4; here #(pits) = 0 and #(peaks) = 0, so 67 is in the sequence.

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

Cf. A296882, A296712, A296880, A296881.

z = 200; b = 9;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296879 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296880 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296881 *)

A296885 Numbers whose base-11 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 A296885-A296887 partition the natural numbers. See the guides at A296712 and A296882.

			The base-11 digits of 1586 are 1,2,1,2; here #(pits) = 1 and #(peaks) = 1, so 1586 is in the sequence.

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

Cf. A296882, A296712, A296886, A296887.

z = 200; b = 11;
d[n_] := Differences[Sign[Differences[IntegerDigits[n, b]]]];
Select[Range [z], Count[d[#], -2] == Count[d[#], 2] &]  (* A296885 *)
Select[Range [z], Count[d[#], -2] < Count[d[#], 2] &]   (* A296886 *)
Select[Range [z], Count[d[#], -2] > Count[d[#], 2] &]   (* A296887 *)

cp's OEIS Frontend

A296751 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

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A296752 Numbers whose base-13 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

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A296754 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

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A296755 Numbers whose base-14 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

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A296757 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

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A296758 Numbers whose base-15 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

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A296760 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

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A296761 Numbers whose base-16 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

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