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A297124 Numbers having an up-first zigzag pattern in base 3; see Comments. 4
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
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.
LINKS
EXAMPLE
Base-3 digits of 1307: 1,2,1,0,1,0,1, with pattern UDUDU, so that 1307 is in the sequence.
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 *)
CROSSREFS
Sequence in context: A101238 A109161 A065908 * A166503 A231720 A134453
KEYWORD
nonn,easy,base
AUTHOR
Clark Kimberling, Jan 13 2018
STATUS
approved

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Last modified March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)