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A297287 Numbers whose base-15 digits have greater up-variation than down-variation; see Comments.

%I A297287 #8 Jan 23 2018 20:36:29
%S A297287 17,18,19,20,21,22,23,24,25,26,27,28,29,33,34,35,36,37,38,39,40,41,42,
%T A297287 43,44,49,50,51,52,53,54,55,56,57,58,59,65,66,67,68,69,70,71,72,73,74,
%U A297287 81,82,83,84,85,86,87,88,89,97,98,99,100,101,102,103,104
%N A297287 Numbers whose base-15 digits have greater up-variation than down-variation; see Comments.
%C A297287 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.
%C A297287 Differs from A296757 first for 227 = 102_15, which has UV= 2 > DV=1 and is in this sequence, but has the same number of rises and falls (so not in A296757). - _R. J. Mathar_, Jan 23 2018
%e A297287 104 in base-15:  6,14 having DV = 0, UV = 8, so that 104 is in the sequence.
%t A297287 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297287 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297287 b = 15; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297287 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297287 Take[Flatten[Position[w, -1]], 120]   (* A297285 *)
%t A297287 Take[Flatten[Position[w, 0]], 120]    (* A297286 *)
%t A297287 Take[Flatten[Position[w, 1]], 120]    (* A297287 *)
%Y A297287 Cf. A297330, A297285, A297286.
%K A297287 nonn,base,easy
%O A297287 1,1
%A A297287 _Clark Kimberling_, Jan 17 2018