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 A297134 Numbers having an up-first zigzag pattern in base 6; see Comments. 4
 8, 9, 10, 11, 15, 16, 17, 22, 23, 29, 48, 49, 51, 52, 53, 54, 55, 56, 58, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 70, 90, 91, 92, 94, 95, 96, 97, 98, 99, 101, 102, 103, 104, 105, 106, 132, 133, 134, 135, 137, 138, 139, 140, 141, 142, 174, 175, 176, 177, 178 (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 A297134-A297136 partition the natural numbers.  See the guide at A297146. LINKS EXAMPLE Base-6 digits of 5000: 3,5,0,5,2, with pattern UDUD, so that 5000 is in the sequence. MATHEMATICA a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300; b = 6; t = Table[a[n, b], {n, 1, 10*z}]; u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *) v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *) Complement[Range[z], Union[u, v]]  (* A297136 *) CROSSREFS Cf. A297135, A297136. Sequence in context: A247631 A297260 A296701 * A247455 A280290 A138581 Adjacent sequences:  A297131 A297132 A297133 * A297135 A297136 A297137 KEYWORD nonn,easy,base AUTHOR Clark Kimberling, Jan 14 2018 STATUS approved

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Last modified December 6 21:48 EST 2019. Contains 329809 sequences. (Running on oeis4.)