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A297272 Numbers whose base-10 digits have greater up-variation than down-variation; see Comments.

%I A297272 #8 Jan 23 2018 19:41:32
%S A297272 12,13,14,15,16,17,18,19,23,24,25,26,27,28,29,34,35,36,37,38,39,45,46,
%T A297272 47,48,49,56,57,58,59,67,68,69,78,79,89,102,103,104,105,106,107,108,
%U A297272 109,112,113,114,115,116,117,118,119,122,123,124,125,126,127,128
%N A297272 Numbers whose base-10 digits have greater up-variation than down-variation; see Comments.
%C A297272 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.
%C A297272 Differs from A071589 first at 1011 which is in A071589 but not in here because UV(1011) = DV(1011)=1. - _R. J. Mathar_, Jan 23 2018
%H A297272 Clark Kimberling, <a href="/A297272/b297272.txt">Table of n, a(n) for n = 1..10000</a>
%e A297272 198765 in base-10:  1,9,8,7,6,5, having DV = 4, UV = 8, so that 198765 is in the sequence.
%t A297272 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297272 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297272 b = 10; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297272 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297272 Take[Flatten[Position[w, -1]], 120]   (* A297270 *)
%t A297272 Take[Flatten[Position[w, 0]], 120]    (* A297271 *)
%t A297272 Take[Flatten[Position[w, 1]], 120]    (* A297272 *)
%Y A297272 Cf. A297330, A297270, A297271.
%K A297272 nonn,base,easy
%O A297272 1,1
%A A297272 _Clark Kimberling_, Jan 16 2018