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A297266 Numbers whose base-8 digits have greater up-variation than down-variation; see Comments.

%I A297266 #4 Jan 16 2018 11:31:55
%S A297266 10,11,12,13,14,15,19,20,21,22,23,28,29,30,31,37,38,39,46,47,55,66,67,
%T A297266 68,69,70,71,74,75,76,77,78,79,82,83,84,85,86,87,90,91,92,93,94,95,98,
%U A297266 99,100,101,102,103,106,107,108,109,110,111,114,115,116,117
%N A297266 Numbers whose base-8 digits have greater up-variation than down-variation; see Comments.
%C A297266 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 A297266 Clark Kimberling, <a href="/A297266/b297266.txt">Table of n, a(n) for n = 1..10000</a>
%e A297266 111 in base-8:  1,5,7, having DV = 0, UV = 6, so that 111 is in the sequence.
%t A297266 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297266 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297266 b = 8; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297266 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297266 Take[Flatten[Position[w, -1]], 120]   (* A297264 *)
%t A297266 Take[Flatten[Position[w, 0]], 120]    (* A297265 *)
%t A297266 Take[Flatten[Position[w, 1]], 120]    (* A297266 *)
%Y A297266 Cf. A297330, A297264, A297265.
%K A297266 nonn,base,easy
%O A297266 1,1
%A A297266 _Clark Kimberling_, Jan 15 2018