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A297290 Numbers whose base-16 digits have greater up-variation than down-variation; see Comments.

%I A297290 #8 Jan 23 2018 20:43:20
%S A297290 18,19,20,21,22,23,24,25,26,27,28,29,30,31,35,36,37,38,39,40,41,42,43,
%T A297290 44,45,46,47,52,53,54,55,56,57,58,59,60,61,62,63,69,70,71,72,73,74,75,
%U A297290 76,77,78,79,86,87,88,89,90,91,92,93,94,95,103,104,105,106
%N A297290 Numbers whose base-16 digits have greater up-variation than down-variation; see Comments.
%C A297290 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 A297290 Differs from A296760 first at 258 = 102_16, which has the same number of rises and falls but UV =2 > DV=1. - _R. J. Mathar_, Jan 23 2018
%H A297290 Clark Kimberling, <a href="/A297290/b297290.txt">Table of n, a(n) for n = 1..10000</a>
%e A297290 106 in base-16:  6,10 having DV = 0, UV = 4, so that 106 is in the sequence.
%t A297290 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297290 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297290 b = 16; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297290 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297290 Take[Flatten[Position[w, -1]], 120]   (* A297288 *)
%t A297290 Take[Flatten[Position[w, 0]], 120]    (* A297289 *)
%t A297290 Take[Flatten[Position[w, 1]], 120]    (* A297290 *)
%Y A297290 Cf. A297330, A297288, A297289.
%K A297290 nonn,base,easy
%O A297290 1,1
%A A297290 _Clark Kimberling_, Jan 17 2018