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.

Previous Showing 11-16 of 16 results.

A297138 Numbers having a down-first zigzag pattern in base 7; 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, 50, 51, 52, 53, 54, 55, 99, 100, 101, 102, 103, 104, 105, 107, 108, 109, 110, 111, 148, 149, 150, 151, 152, 153, 154, 156, 157, 158, 159, 160, 161, 162, 164, 165, 166, 167
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 5000: 2,0,4,0,2, with pattern DUDU, so that 5000 is in the sequence.

Crossrefs

Cf. A297137, A297139.

Programs

  • 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 *)

A297140 Numbers having an up-first zigzag pattern in base 8; see Comments.

Original entry on oeis.org

10, 11, 12, 13, 14, 15, 19, 20, 21, 22, 23, 28, 29, 30, 31, 37, 38, 39, 46, 47, 55, 80, 81, 83, 84, 85, 86, 87, 88, 89, 90, 92, 93, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 107, 108, 110, 111, 112, 113, 114, 115, 116, 117, 119, 120, 121, 122
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 A297140-A297142 partition the natural numbers. See the guide at A297146.

Examples

			Base-8 digits of 3575: 6, 7, 6, 7, with pattern UDU, so that 3575 is in the sequence.

Crossrefs

Cf. A297141, A297142.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 8; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297140 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297141 *)
Complement[Range[z], Union[u, v]]  (* A297142 *)

A297141 Numbers having a down-first zigzag pattern in base 8; see Comments.

Original entry on oeis.org

8, 16, 17, 24, 25, 26, 32, 33, 34, 35, 40, 41, 42, 43, 44, 48, 49, 50, 51, 52, 53, 56, 57, 58, 59, 60, 61, 62, 65, 66, 67, 68, 69, 70, 71, 129, 130, 131, 132, 133, 134, 135, 136, 138, 139, 140, 141, 142, 143, 193, 194, 195, 196, 197, 198, 199, 200, 202, 203
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 A297140-A297142 partition the natural numbers. See the guide at A297146.

Examples

			Base-8 digits of 4599: 1,0,7,6,7, with pattern DUDU, so that 4599 is in the sequence.

Crossrefs

Cf. A297140, A297142.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 8; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297140 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297141 *)
Complement[Range[z], Union[u, v]]  (* A297142 *)

A297143 Numbers having an up-first zigzag pattern in base 9; see Comments.

Original entry on oeis.org

11, 12, 13, 14, 15, 16, 17, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 41, 42, 43, 44, 51, 52, 53, 61, 62, 71, 99, 100, 102, 103, 104, 105, 106, 107, 108, 109, 110, 112, 113, 114, 115, 116, 117, 118, 119, 120, 122, 123, 124, 125, 126, 127, 128, 129, 130
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 A297143-A297145 partition the natural numbers. See the guide at A297146.

Examples

			Base-9 digits of 10000: 1,4,6,4,1, with pattern UD, so that 10000 is in the sequence.

Crossrefs

Cf. A297144, A297145.

Programs

  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 9; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297143 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297144 *)
Complement[Range[z], Union[u, v]]  (* A297145 *)

A297144 Numbers having a down-first zigzag pattern in base 9; see Comments.

Original entry on oeis.org

9, 18, 19, 27, 28, 29, 36, 37, 38, 39, 45, 46, 47, 48, 49, 54, 55, 56, 57, 58, 59, 63, 64, 65, 66, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 82, 83, 84, 85, 86, 87, 88, 89, 163, 164, 165, 166, 167, 168, 169, 170, 171, 173, 174, 175, 176, 177, 178, 179, 244
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 A297143-A297145 partition the natural numbers. See the guide at A297146.

Examples

			Base-9 digits of 7280: 1,0,8,7,8, with pattern DUDU, so that 7280 is in the sequence.

Links

Crossrefs

Cf. A297143, A297145.

Programs

  • Maple
    filter:= proc(n)  local L;
L:= convert(n,base,9);
not has(L[2..-1]-L[1..-2],0) and L[-1]>L[-2]
end proc:
select(filter, [$9..1000]); # Robert Israel, Dec 06 2018
  • Mathematica
    a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
b = 9; t = Table[a[n, b], {n, 1, 10*z}];
u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297143 *)
v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297144 *)
Complement[Range[z], Union[u, v]]  (* A297145 *)

A297148 Numbers whose base-10 digits d(m), d(m-1),..., d(0) have m=0 or else d(i) = d(i+1) for some i in {0,1,...,m-1}.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 100, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 122, 133, 144, 155, 166, 177, 188, 199, 200, 211, 220, 221, 222, 223, 224, 225, 226, 227, 228, 229, 233, 244, 255, 266, 277, 288, 299, 300
Offset: 1

Views

Author

Clark Kimberling, Jan 15 2018

Keywords

Comments

These numbers comprise the complement of the set of numbers in the union of A297146 and A297147.
Differs from A044821 first for 1001, which is in this sequence but not in A044821. - R. J. Mathar, Jan 17 2018

Examples

			Base-10 digits of 65536: 6,5,5,3,6, so that 65536 is in the sequence.

Crossrefs

Cf. A297146, A297147.

Programs

  • Maple
    read("transforms") :
isA297148 := proc(n)
    local dgs,ud;
    dgs := convert(n,base,10) ;
    if nops(dgs) < 2 then
        return true;
    end if;
    if 0 in DIFF(dgs) then
        true;
    else
        false;
    end if;
end proc:
for n from 1 to 300 do
    if isA297148(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 = 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 *)
Previous Showing 11-16 of 16 results.

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