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A297269 Numbers whose base-9 digits have greater up-variation than down-variation; see Comments.

%I A297269 #4 Jan 16 2018 11:32:20
%S A297269 11,12,13,14,15,16,17,21,22,23,24,25,26,31,32,33,34,35,41,42,43,44,51,
%T A297269 52,53,61,62,71,83,84,85,86,87,88,89,92,93,94,95,96,97,98,101,102,103,
%U A297269 104,105,106,107,110,111,112,113,114,115,116,119,120,121,122
%N A297269 Numbers whose base-9 digits have greater up-variation than down-variation; see Comments.
%C A297269 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 A297269 Clark Kimberling, <a href="/A297269/b297269.txt">Table of n, a(n) for n = 1..10000</a>
%e A297269 122 in base-9:  1,4,5, having DV = 0, UV = 4, so that 122 is in the sequence.
%t A297269 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297269 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297269 b = 9; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297269 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297269 Take[Flatten[Position[w, -1]], 120]   (* A297267 *)
%t A297269 Take[Flatten[Position[w, 0]], 120]    (* A297268 *)
%t A297269 Take[Flatten[Position[w, 1]], 120]    (* A297269 *)
%Y A297269 Cf. A297330, A297267, A297268.
%K A297269 nonn,base,easy
%O A297269 1,1
%A A297269 _Clark Kimberling_, Jan 15 2018