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A297288 Numbers whose base-16 digits have greater down-variation than up-variation; see Comments.

%I A297288 #8 Jan 23 2018 20:38:35
%S A297288 16,32,33,48,49,50,64,65,66,67,80,81,82,83,84,96,97,98,99,100,101,112,
%T A297288 113,114,115,116,117,118,128,129,130,131,132,133,134,135,144,145,146,
%U A297288 147,148,149,150,151,152,160,161,162,163,164,165,166,167,168,169
%N A297288 Numbers whose base-16 digits have greater down-variation than up-variation; see Comments.
%C A297288 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 A297288 Differs from A296761 first at 288 = 120_16, which has the same number of rises and falls (so not in A296761) but DV =2 > UV =1 (so in this sequence). - _R. J. Mathar_, Jan 23 2018
%H A297288 Clark Kimberling, <a href="/A297288/b297288.txt">Table of n, a(n) for n = 1..10000</a>
%e A297288 169 in base-16:  10,9 having DV = 1, UV = 0, so that 169 is in the sequence.
%t A297288 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297288 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297288 b = 16; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297288 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297288 Take[Flatten[Position[w, -1]], 120]   (* A297288 *)
%t A297288 Take[Flatten[Position[w, 0]], 120]    (* A297289 *)
%t A297288 Take[Flatten[Position[w, 1]], 120]    (* A297290 *)
%Y A297288 Cf. A297330, A297289, A297290.
%K A297288 nonn,base,easy
%O A297288 1,1
%A A297288 _Clark Kimberling_, Jan 17 2018