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 A297128 Numbers having an up-first zigzag pattern in base 4; see Comments. 4
 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 (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 A297128..A297130 partition the natural numbers. See the guide at A297146. LINKS EXAMPLE Base-4 digits of 3003: 2,3,2,3,2,3, with pattern UDUDU, so that 3003 is in the sequence. 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 *) CROSSREFS Cf. A297129, A297130. Sequence in context: A347512 A296695 A228948 * A035110 A011990 A105085 Adjacent sequences: A297125 A297126 A297127 * A297129 A297130 A297131 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Jan 13 2018 STATUS approved

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Last modified March 20 05:48 EDT 2023. Contains 361359 sequences. (Running on oeis4.)