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A297259 Numbers whose base-6 digits have equal down-variation and up-variation; see Comments.

%I A297259 #4 Jan 15 2018 21:08:28
%S A297259 1,2,3,4,5,7,14,21,28,35,37,43,49,55,61,67,74,80,86,92,98,104,111,117,
%T A297259 123,129,135,141,148,154,160,166,172,178,185,191,197,203,209,215,217,
%U A297259 223,229,235,241,247,253,259,265,271,277,283,289,295,301,307,313
%N A297259 Numbers whose base-6 digits have equal down-variation and up-variation; see Comments.
%C A297259 Suppose that n has base-b digits b(m), b(m-1), ..., b(0).  The base-b down-variation of n is the sum DV(n,b) of all d(i)-d(i-1) for which d(i) > d(i-1); the base-b up-variation of n is the sum UV(n,b) of all d(k-1)-d(k) for which d(k) < d(k-1).  The total base-b variation of n is the sum TV(n,b) = DV(n,b) + UV(n,b).  See the guide at A297330.
%H A297259 Clark Kimberling, <a href="/A297259/b297259.txt">Table of n, a(n) for n = 1..10000</a>
%e A297259 313 in base-6:  1,2,4,1, having DV = 3, UV = 3, so that 313 is in the sequence.
%t A297259 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297259 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297259 b = 6; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297259 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297259 Take[Flatten[Position[w, -1]], 120]   (* A297258 *)
%t A297259 Take[Flatten[Position[w, 0]], 120]    (* A297259 *)
%t A297259 Take[Flatten[Position[w, 1]], 120]    (* A297260 *)
%Y A297259 Cf. A297330, A297258, A297260.
%K A297259 nonn,base,easy
%O A297259 1,2
%A A297259 _Clark Kimberling_, Jan 15 2018