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A297267 Numbers whose base-9 digits have greater down-variation than up-variation; see Comments.

%I A297267 #4 Jan 16 2018 11:32:03
%S A297267 9,18,19,27,28,29,36,37,38,39,45,46,47,48,49,54,55,56,57,58,59,63,64,
%T A297267 65,66,67,68,69,72,73,74,75,76,77,78,79,81,90,99,108,117,126,135,144,
%U A297267 153,162,163,171,172,180,181,189,190,198,199,207,208,216,217,225
%N A297267 Numbers whose base-9 digits have greater down-variation than up-variation; see Comments.
%C A297267 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 A297267 Clark Kimberling, <a href="/A297267/b297267.txt">Table of n, a(n) for n = 1..10000</a>
%e A297267 225 in base-9:  2,7,0, having DV = 7, UV = 5, so that 225 is in the sequence.
%t A297267 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297267 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297267 b = 9; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297267 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297267 Take[Flatten[Position[w, -1]], 120]   (* A297267 *)
%t A297267 Take[Flatten[Position[w, 0]], 120]    (* A297268 *)
%t A297267 Take[Flatten[Position[w, 1]], 120]    (* A297269 *)
%Y A297267 Cf. A297330, A297268, A297269.
%K A297267 nonn,base,easy
%O A297267 1,1
%A A297267 _Clark Kimberling_, Jan 15 2018