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A297264 Numbers whose base-8 digits have greater down-variation than up-variation; see Comments.

%I A297264 #4 Jan 16 2018 11:31:39
%S A297264 8,16,17,24,25,26,32,33,34,35,40,41,42,43,44,48,49,50,51,52,53,56,57,
%T A297264 58,59,60,61,62,64,72,80,88,96,104,112,120,128,129,136,137,144,145,
%U A297264 152,153,160,161,168,169,176,177,184,185,192,193,194,200,201,202
%N A297264 Numbers whose base-8 digits have greater down-variation than up-variation; see Comments.
%C A297264 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 A297264 Clark Kimberling, <a href="/A297264/b297264.txt">Table of n, a(n) for n = 1..10000</a>
%e A297264 202 in base-8:  3,1,2, having DV = 2, UV = 1, so that 202 is in the sequence.
%t A297264 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297264 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297264 b = 8; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297264 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297264 Take[Flatten[Position[w, -1]], 120]   (* A297264 *)
%t A297264 Take[Flatten[Position[w, 0]], 120]    (* A297265 *)
%t A297264 Take[Flatten[Position[w, 1]], 120]    (* A297266 *)
%Y A297264 Cf. A297330, A297265, A297266.
%K A297264 nonn,base,easy
%O A297264 1,1
%A A297264 _Clark Kimberling_, Jan 15 2018