cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A296696 Numbers whose base-4 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

4, 8, 9, 12, 13, 14, 16, 20, 32, 36, 37, 40, 41, 48, 52, 53, 56, 57, 58, 60, 61, 62, 64, 68, 72, 73, 76, 77, 78, 80, 84, 100, 116, 120, 121, 128, 132, 136, 137, 140, 141, 142, 144, 145, 146, 147, 148, 149, 152, 153, 156, 157, 158, 160, 164, 165, 168, 169
Offset: 1

Views

Author

Clark Kimberling, Dec 21 2017

Keywords

Comments

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.

Examples

			The base-4 digits of 196 are 3,0,1,0; here #(rises) = 1 and #(falls) = 2, so 196 is in the sequence.

Links

Crossrefs

Cf. A296694, A296695, A296712.

Programs

  • Mathematica
    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 *)

Extensions

Example corrected by Harvey P. Dale, Sep 04 2018

A296697 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 6, 12, 18, 24, 26, 27, 28, 29, 31, 35, 36, 40, 41, 42, 45, 46, 47, 48, 51, 52, 53, 54, 57, 58, 59, 62, 65, 66, 67, 70, 71, 72, 73, 76, 77, 78, 79, 82, 83, 84, 88, 89, 93, 95, 96, 97, 98, 101, 102, 103, 104, 107, 108, 109, 113, 114, 119, 124, 126
Offset: 1

Views

Author

Clark Kimberling, Dec 21 2017

Keywords

Comments

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 A296697-A296699 partition the natural numbers. See the guide at A296712.

Examples

			The base-5 digits of 126 are 1,0,0,1; here #(rises) = 1 and #(falls) = 1, so 126 is in the sequence.

Links

Crossrefs

Cf. A296698, A296699, A296712.

Programs

  • Mathematica
    z = 200; b = 5; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296697 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296698 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296699 *)
Select[Range[130],Total[Sign[Differences[IntegerDigits[#,5]]]]==0&] (* Harvey P. Dale, Jul 30 2019 *)

A296698 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

7, 8, 9, 13, 14, 19, 32, 33, 34, 37, 38, 39, 43, 44, 49, 63, 64, 68, 69, 74, 94, 99, 132, 133, 134, 138, 139, 144, 157, 158, 159, 162, 163, 164, 168, 169, 174, 176, 177, 178, 179, 182, 183, 184, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199
Offset: 1

Views

Author

Clark Kimberling, Dec 21 2017

Keywords

Comments

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 A296697-A296699 partition the natural numbers. See the guide at A296712.

Examples

			The base-5 digits of 199 are 1,2,4,4; here #(rises) = 2 and #(falls) = 0, so 199 is in the sequence.

Links

Crossrefs

Cf. A296697, A296699, A296712.

Programs

  • Mathematica
    z = 200; b = 5; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296697 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296698 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296699 *)

A296699 Numbers whose base-5 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 25, 30, 50, 55, 56, 60, 61, 75, 80, 81, 85, 86, 87, 90, 91, 92, 100, 105, 106, 110, 111, 112, 115, 116, 117, 118, 120, 121, 122, 123, 125, 130, 135, 136, 140, 141, 142, 145, 146, 147, 148, 150, 155, 180, 205, 210, 211
Offset: 1

Views

Author

Clark Kimberling, Dec 21 2017

Keywords

Comments

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 A296697-A296699 partition the natural numbers. See the guide at A296712.

Examples

			The base-5 digits of 211 are 1,3,2,1; here #(rises) = 1 and #(falls) = 2, so 211 is in the sequence.

Links

Crossrefs

Cf. A296697, A296698, A296712.

Programs

  • Mathematica
    z = 200; b = 5; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296697 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296698 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296699 *)

A296701 Numbers whose base-6 digits d(m), d(m-1), ... d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 44, 45, 46, 47, 50, 51, 52, 53, 57, 58, 59, 64, 65, 71, 87, 88, 89, 93, 94, 95, 100, 101, 107, 130, 131, 136, 137, 143, 173, 179, 224, 225, 226, 227, 231, 232, 233, 238, 239, 245, 260, 261, 262, 263, 266, 267, 268, 269
Offset: 1

Views

Author

Clark Kimberling, Jan 07 2018

Keywords

Comments

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 A296700-A296702 partition the natural numbers. See the guide at A296712.

Examples

			The base-6 digits of 269 are 1, 1, 2, 5; here #(rises) = 2 and #(falls) = 0, so 269 is in the sequence.

Links

Crossrefs

Cf. A296700, A296702, A296712.

Programs

  • Mathematica
    z = 200; b = 6; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296700 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296701 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296702 *)

A296702 Numbers whose base-6 digits d(m), d(m-1), ... d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 36, 42, 72, 78, 79, 84, 85, 108, 114, 115, 120, 121, 122, 126, 127, 128, 144, 150, 151, 156, 157, 158, 162, 163, 164, 165, 168, 169, 170, 171, 180, 186, 187, 192, 193, 194, 198, 199, 200, 201, 204
Offset: 1

Views

Author

Clark Kimberling, Jan 07 2018

Keywords

Comments

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 A296700-A296702 partition the natural numbers. See the guide at A296712.

Examples

			The base-6 digits of 224 are 5,4,0; here #(rises) = 0 and #(falls) = 2, so 204 is in the sequence.

Links

Crossrefs

Cf. A296700, A296701, A296712.

Programs

  • Mathematica
    z = 200; b = 6; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296700 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296701 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296702 *)

A296703 Numbers whose base-7 digits d(m), d(m-1), ... d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 8, 16, 24, 32, 40, 48, 50, 51, 52, 53, 54, 55, 57, 63, 64, 70, 71, 72, 77, 78, 79, 80, 84, 85, 86, 87, 88, 91, 92, 93, 94, 95, 96, 99, 100, 101, 102, 103, 104, 107, 108, 109, 110, 111, 114, 119, 120, 121, 126, 127, 128, 129, 133, 134, 135
Offset: 1

Views

Author

Clark Kimberling, Jan 07 2018

Keywords

Comments

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 A296703-A296705 partition the natural numbers. See the guide at A296712.

Examples

			The base-7 digits of 135 are 2,5,2; here #(rises) = 1 and #(falls) = 1, so 135 is in the sequence.

Links

Crossrefs

Cf. A296704, A296705, A296712.

Programs

  • Mathematica
    z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296704 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296705 *)

A296704 Numbers whose base-7 digits d(m), d(m-1), ..., d(0) have #(rises) > #(falls); see Comments.

Original entry on oeis.org

9, 10, 11, 12, 13, 17, 18, 19, 20, 25, 26, 27, 33, 34, 41, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 73, 74, 75, 76, 81, 82, 83, 89, 90, 97, 115, 116, 117, 118, 122, 123, 124, 125, 130, 131, 132, 138, 139, 146, 172, 173, 174, 179, 180, 181, 187, 188, 195, 229
Offset: 1

Views

Author

Clark Kimberling, Jan 08 2018

Keywords

Comments

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 A296703-A296705 partition the natural numbers. See the guide at A296712.

Examples

			The base-7 digits of 229 are 4,4,5; here #(rises) = 1 and #(falls) = 0, so 229 is in the sequence.

Links

Crossrefs

Cf. A296704, A296705, A296712.

Programs

  • Mathematica
    z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296704 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296705 *)

A296705 Numbers whose base-7 digits d(m), d(m-1), ..., d(0) have #(rises) < #(falls); see Comments.

Original entry on oeis.org

7, 14, 15, 21, 22, 23, 28, 29, 30, 31, 35, 36, 37, 38, 39, 42, 43, 44, 45, 46, 47, 49, 56, 98, 105, 106, 112, 113, 147, 154, 155, 161, 162, 163, 168, 169, 170, 196, 203, 204, 210, 211, 212, 217, 218, 219, 220, 224, 225, 226, 227, 245, 252, 253, 259, 260, 261
Offset: 1

Views

Author

Clark Kimberling, Jan 08 2018

Keywords

Comments

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 A296703-A296705 partition the natural numbers. See the guide at A296712.

Examples

			The base-7 digits of 261 are 5,2,2; here #(rises) = 0 and #(falls) = 2, so 261 is in the sequence.

Links

Crossrefs

Cf. A296703, A296704, A296712.

Programs

  • Mathematica
    z = 200; b = 7; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296703 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296704 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296705 *)

A296706 Numbers whose base-8 digits d(m), d(m-1), ..., d(0) have #(rises) = #(falls); see Comments.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 9, 18, 27, 36, 45, 54, 63, 65, 66, 67, 68, 69, 70, 71, 73, 80, 81, 88, 89, 90, 96, 97, 98, 99, 104, 105, 106, 107, 108, 112, 113, 114, 115, 116, 117, 120, 121, 122, 123, 124, 125, 126, 129, 130, 131, 132, 133, 134, 135, 138, 139, 140
Offset: 1

Views

Author

Clark Kimberling, Jan 08 2018

Keywords

Comments

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 A296706-A296707 partition the natural numbers. See the guide at A296712.

Examples

			The base-8 digits of 140 are 2,1,4; here #(rises) = 1 and #(falls) = 1, so 140 is in the sequence.

Links

Crossrefs

Cf. A296707, A296708, A296712.

Programs

  • Mathematica
    z = 200; b = 8; d[n_] := Sign[Differences[IntegerDigits[n, b]]];
Select[Range [z], Count[d[#], -1] == Count[d[#], 1] &] (* A296706 *)
Select[Range [z], Count[d[#], -1] < Count[d[#], 1] &]  (* A296707 *)
Select[Range [z], Count[d[#], -1] > Count[d[#], 1] &]  (* A296708 *)
Previous Showing 31-40 of 115 results. Next

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