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%I #4 Jan 15 2018 21:08:35
%S 8,9,10,11,15,16,17,22,23,29,38,39,40,41,44,45,46,47,50,51,52,53,56,
%T 57,58,59,62,63,64,65,68,69,70,71,75,76,77,81,82,83,87,88,89,93,94,95,
%U 99,100,101,105,106,107,112,113,118,119,124,125,130,131,136
%N Numbers whose base-6 digits have greater up-variation than down-variation; see Comments.
%C 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 Clark Kimberling, <a href="/A297260/b297260.txt">Table of n, a(n) for n = 1..10000</a>
%e 136 in base-6: 3,4,4, having DV = 0, UV = 1, so that 136 is in the sequence.
%t g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t b = 6; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t Take[Flatten[Position[w, -1]], 120] (* A297258 *)
%t Take[Flatten[Position[w, 0]], 120] (* A297259 *)
%t Take[Flatten[Position[w, 1]], 120] (* A297260 *)
%Y Cf. A297330, A297258, A297259.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 15 2018
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