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.

Showing 1-10 of 16 results. Next

A297147 Numbers having a down-first zigzag pattern in base 10; see Comments.

Original entry on oeis.org

10, 20, 21, 30, 31, 32, 40, 41, 42, 43, 50, 51, 52, 53, 54, 60, 61, 62, 63, 64, 65, 70, 71, 72, 73, 74, 75, 76, 80, 81, 82, 83, 84, 85, 86, 87, 90, 91, 92, 93, 94, 95, 96, 97, 98, 101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297146-A297148 partition the natural numbers. See the guide at A297146.

Examples

			Base-10 digits of 65498: 6,5,4,9,8, with pattern DUD, so that 65498 is in the sequence.

Crossrefs

Cf. A297146, A297148.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 10; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297146 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297147 *)
Complement[Range[z], Union[u, v]]  (* A297148 *)

A297124 Numbers having an up-first zigzag pattern in base 3; see Comments.

Original entry on oeis.org

5, 15, 16, 46, 47, 48, 50, 138, 140, 141, 142, 145, 146, 150, 151, 415, 416, 420, 421, 424, 425, 426, 428, 435, 437, 438, 439, 451, 452, 453, 455, 1245, 1247, 1248, 1249, 1261, 1262, 1263, 1265, 1272, 1274, 1275, 1276, 1279, 1280, 1284, 1285, 1306, 1307
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1), ..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297124..A297127 partition the natural numbers. See the guide at A297146.

Examples

			Base-3 digits of 1307: 1,2,1,0,1,0,1, with pattern UDUDU, so that 1307 is in the sequence.

Crossrefs

Cf. A297125, A297126.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 3; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297124 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297125 *)
Complement[Range[z], Union[u, v]]  (* A297126 *)

A297125 Numbers having a down-first zigzag pattern in base 3; see Comments.

Original entry on oeis.org

3, 6, 7, 10, 11, 19, 20, 21, 23, 30, 32, 33, 34, 57, 59, 60, 61, 64, 65, 69, 70, 91, 92, 96, 97, 100, 101, 102, 104, 172, 173, 177, 178, 181, 182, 183, 185, 192, 194, 195, 196, 208, 209, 210, 212, 273, 275, 276, 277, 289, 290, 291, 293, 300, 302, 303, 304
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1), ..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297124..A297127 partition the natural numbers. See the guide at A297146.

Examples

			Base-3 digits of 307: 1,0,2,1,0,1, with pattern DUDU, so that 307 is in the sequence.

Crossrefs

Cf. A297124, A297126.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 3; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297124 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297125 *)
Complement[Range[z], Union[u, v]]  (* A297126 *)

A297128 Numbers having an up-first zigzag pattern in base 4; see Comments.

Original entry on oeis.org

6, 7, 11, 24, 25, 27, 28, 29, 30, 44, 45, 46, 97, 98, 99, 100, 102, 103, 108, 109, 110, 113, 114, 115, 116, 118, 119, 120, 121, 123, 177, 178, 179, 180, 182, 183, 184, 185, 187, 388, 390, 391, 392, 393, 395, 396, 397, 398, 401, 402, 403, 408, 409, 411, 412
Offset: 1

Views

Author

Clark Kimberling, Jan 13 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1), ..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297128..A297130 partition the natural numbers. See the guide at A297146.

Examples

			Base-4 digits of 3003: 2,3,2,3,2,3, with pattern UDUDU, so that 3003 is in the sequence.

Crossrefs

Cf. A297129, A297130.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 4; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297128 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297129 *)
Complement[Range[z], Union[u, v]]  (* A297130 *)

A297129 Numbers having a down-first zigzag pattern in base 4; see Comments.

Original entry on oeis.org

4, 8, 9, 12, 13, 14, 17, 18, 19, 33, 34, 35, 36, 38, 39, 49, 50, 51, 52, 54, 55, 56, 57, 59, 68, 70, 71, 72, 73, 75, 76, 77, 78, 132, 134, 135, 136, 137, 139, 140, 141, 142, 145, 146, 147, 152, 153, 155, 156, 157, 158, 196, 198, 199, 200, 201, 203, 204, 205
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297128-A297130 partition the natural numbers. See the guide at A297146.

Examples

			Base-4 digits of 5000: 1,0,3,2,0,2,0, with pattern DUDUD, so that 5000 is in the sequence.

Crossrefs

Cf. A297128, A297130.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 4; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297128 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297129 *)
Complement[Range[z], Union[u, v]]  (* A297130 *)

A297131 Numbers having an up-first zigzag pattern in base 5; see Comments.

Original entry on oeis.org

7, 8, 9, 13, 14, 19, 35, 36, 38, 39, 40, 41, 42, 44, 45, 46, 47, 48, 65, 66, 67, 69, 70, 71, 72, 73, 95, 96, 97, 98, 176, 177, 178, 179, 180, 182, 183, 184, 190, 191, 192, 194, 195, 196, 197, 198, 201, 202, 203, 204, 205, 207, 208, 209, 210, 211, 213, 214
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297131-A297133 partition the natural numbers. See the guide at A297146.

Examples

			Base-5 digits of 4973: 1,2,4,3,4,3, with pattern UDUD, so that 4973 is in the sequence.

Crossrefs

Cf. A297132, A297133.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 5; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297131 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297132 *)
Complement[Range[z], Union[u, v]]  (* A297133 *)

A297132 Numbers having a down-first zigzag pattern in base 5; see Comments.

Original entry on oeis.org

5, 10, 11, 15, 16, 17, 20, 21, 22, 23, 26, 27, 28, 29, 51, 52, 53, 54, 55, 57, 58, 59, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 88, 89, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 113, 114, 115, 116, 117, 119, 130, 132, 133, 134, 135, 136, 138, 139, 140
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297131-A297133 partition the natural numbers. See the guide at A297146.

Examples

			Base-5 digits of 3723: 1,0,4,3,4,3, with pattern DUDUD, so that 3723 is in the sequence.

Crossrefs

Cf. A297131, A297133.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 5; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297131 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297132 *)
Complement[Range[z], Union[u, v]]  (* A297133 *)

A297134 Numbers having an up-first zigzag pattern in base 6; see Comments.

Original entry on oeis.org

8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 174, 175, 176, 177, 178
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297134-A297136 partition the natural numbers. See the guide at A297146.

Examples

			Base-6 digits of 5000: 3,5,0,5,2, with pattern UDUD, so that 5000 is in the sequence.

Crossrefs

Cf. A297135, A297136.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 6; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *)
Complement[Range[z], Union[u, v]]  (* A297136 *)

A297135 Numbers having a down-first zigzag pattern in base 6; see Comments.

Original entry on oeis.org

6, 12, 13, 18, 19, 20, 24, 25, 26, 27, 30, 31, 32, 33, 34, 37, 38, 39, 40, 41, 73, 74, 75, 76, 77, 78, 80, 81, 82, 83, 109, 110, 111, 112, 113, 114, 116, 117, 118, 119, 120, 121, 123, 124, 125, 145, 146, 147, 148, 149, 150, 152, 153, 154, 155, 156, 157, 159
Offset: 1

Views

Author

Clark Kimberling, Jan 14 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297134-A297136 partition the natural numbers. See the guide at A297146.

Examples

			Base-6 digits of 4529: 3,2,5,4,5, with pattern DUDU, so that 4529 is in the sequence.

Crossrefs

Cf. A297134, A297136.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 6; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *)
Complement[Range[z], Union[u, v]]  (* A297136 *)

A297137 Numbers having an up-first zigzag pattern in base 7; see Comments.

Original entry on oeis.org

9, 10, 11, 12, 13, 17, 18, 19, 20, 25, 26, 27, 33, 34, 41, 63, 64, 66, 67, 68, 69, 70, 71, 72, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 85, 86, 87, 88, 90, 91, 92, 93, 94, 95, 96, 119, 120, 121, 123, 124, 125, 126, 127, 128, 129, 131, 132, 133, 134, 135, 136
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2018

Keywords

Comments

A number n having base-b digits d(m), d(m-1),..., d(0) such that d(i) != d(i+1) for 0 <= i < m shows a zigzag pattern of one or more segments, in the following sense. Writing U for up and D for down, there are two kinds of patterns: U, UD, UDU, UDUD, ... and D, DU, DUD, DUDU, ... . In the former case, we say n has an "up-first zigzag pattern in base b"; in the latter, a "down-first zigzag pattern in base b". Example: 2,4,5,3,0,1,4,2 has segments 2,4,5; 5,3,0; 0,1,4; and 4,2, so that 24530142, with pattern UDUD, has an up-first zigzag pattern in base 10, whereas 4,2,5,3,0,1,4,2 has a down-first pattern. The sequences A297137-A297139 partition the natural numbers. See the guide at A297146.

Examples

			Base-7 digits of 4751: 1,6,5,6,5, with pattern UDUD, so that 4751 is in the sequence.

Links

Crossrefs

Cf. A297138, A297139.

Programs

  • Maple
    read("transforms") :
isA297137 := proc(n)
    local dgs,ud;
    dgs := convert(n,base,7) ;
    if nops(dgs) < 2 then
        return false;
    end if;
    ud := DIFF(dgs) ;
    if 0 in ud then
        return false;
    else
        simplify( op(-1,ud) < 0) ;
    end if;
end proc:
for n from 1 to 200 do
    if isA297137(n) then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, Jan 18 2018
  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 7; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297137 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297138 *)
Complement[Range[z], Union[u, v]]  (* A297139 *)
Showing 1-10 of 16 results. Next

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