A297125 -id:A297125 - cp's OEIS frontend

A297146 Numbers having an up-first zigzag pattern in base 10; see Comments.

12, 13, 14, 15, 16, 17, 18, 19, 23, 24, 25, 26, 27, 28, 29, 34, 35, 36, 37, 38, 39, 45, 46, 47, 48, 49, 56, 57, 58, 59, 67, 68, 69, 78, 79, 89, 120, 121, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 145

Offset: 1

Clark Kimberling, Jan 15 2018

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. In the following guide, column four, "complement" means the sequence of natural numbers not in the corresponding sequences in columns 2 and 3.
***
Base      up-first    down-first  complement
         (none)     A000975     A107907
        A297124     A297125     A297126
        A297128     A297129     A297130
        A297131     A297132     A297133
        A297134     A297135     A297136
        A297137     A297138     A297139
        A297140     A297141     A297142
        A297143     A297144     A297145
       A297146     A297147     A297148

			Base-10 digits of 59898: 5,9,8,9,8, with pattern UDUD, so that 59898 is in the sequence.

Cf. A297147, A297148.

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

Clark Kimberling, Jan 13 2018

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.

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

Cf. A297125, A297126.

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 *)

A297126 Numbers whose base-3 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, 4, 8, 9, 12, 13, 14, 17, 18, 22, 24, 25, 26, 27, 28, 29, 31, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 49, 51, 52, 53, 54, 55, 56, 58, 62, 63, 66, 67, 68, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 93, 94, 95

Offset: 1

Clark Kimberling, Apr 10 2018

These numbers comprise the complement of the set of numbers in the union of A297124 and A297125.

			Base-3 digits of 95: 1,0,1,1,2, so that 95 is in the sequence.

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A297124, A297125.

filter:= proc(n) local L;
  L:= convert(n,base,3);
  member(0,L[2..-1]-L[1..-2])
end proc:
filter(1):= true: filter(2):= true:
select(filter, [$1..100]); # Robert Israel, Apr 12 2018

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 *)

3 removed by Robert Israel, Apr 12 2018

cp's OEIS Frontend

A297146 Numbers having an up-first zigzag pattern in base 10; see Comments.

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

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

Views

Author

Keywords

Comments

Examples

Crossrefs

Programs

Mathematica

A297126 Numbers whose base-3 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}.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

Extensions