cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A297134 Numbers having an up-first zigzag pattern in base 6; see Comments.

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%I A297134 #6 Jan 14 2018 23:02:01
%S A297134 8,9,10,11,15,16,17,22,23,29,48,49,51,52,53,54,55,56,58,59,60,61,62,
%T A297134 63,65,66,67,68,69,70,90,91,92,94,95,96,97,98,99,101,102,103,104,105,
%U A297134 106,132,133,134,135,137,138,139,140,141,142,174,175,176,177,178
%N A297134 Numbers having an up-first zigzag pattern in base 6; see Comments.
%C A297134 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.
%e A297134 Base-6 digits of 5000: 3,5,0,5,2, with pattern UDUD, so that 5000 is in the sequence.
%t A297134 a[n_, b_] := Sign[Differences[IntegerDigits[n, b]]]; z = 300;
%t A297134 b = 6; t = Table[a[n, b], {n, 1, 10*z}];
%t A297134 u = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == 1 &]   (* A297134 *)
%t A297134 v = Select[Range[z], ! MemberQ[t[[#]], 0] && First[t[[#]]] == -1 &]  (* A297135 *)
%t A297134 Complement[Range[z], Union[u, v]]  (* A297136 *)
%Y A297134 Cf. A297135, A297136.
%K A297134 nonn,easy,base
%O A297134 1,1
%A A297134 _Clark Kimberling_, Jan 14 2018