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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 Cf. A297125, A297126. Sequence in context: A101238 A109161 A065908 * A166503 A231720 A134453 Adjacent sequences:  A297121 A297122 A297123 * A297125 A297126 A297127 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Jan 13 2018 STATUS approved

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Last modified June 30 18:52 EDT 2022. Contains 354945 sequences. (Running on oeis4.)