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A297270 Numbers whose base-10 digits have greater down-variation than up-variation; see Comments.

%I A297270 #9 Jan 23 2018 19:35:11
%S A297270 10,20,21,30,31,32,40,41,42,43,50,51,52,53,54,60,61,62,63,64,65,70,71,
%T A297270 72,73,74,75,76,80,81,82,83,84,85,86,87,90,91,92,93,94,95,96,97,98,
%U A297270 100,110,120,130,140,150,160,170,180,190,200,201,210,211,220,221
%N A297270 Numbers whose base-10 digits have greater down-variation than up-variation; see Comments.
%C A297270 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 A297270 Differs first from A071590 at 1101, which is in A071590, but not in here because UV(1101) = DV(1101). - _R. J. Mathar_, Jan 23 2018
%H A297270 Clark Kimberling, <a href="/A297270/b297270.txt">Table of n, a(n) for n = 1..10000</a>
%e A297270 6151413121 in base-10:  6,1,5,1,4,1,3,1,2,1, having DV = 15, UV = 10, so that 6151413121 is in the sequence.
%t A297270 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297270 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297270 b = 10; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297270 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297270 Take[Flatten[Position[w, -1]], 120]   (* A297270 *)
%t A297270 Take[Flatten[Position[w, 0]], 120]    (* A297271 *)
%t A297270 Take[Flatten[Position[w, 1]], 120]    (* A297272 *)
%Y A297270 Cf. A297330, A297271, A297272.
%K A297270 nonn,base,easy
%O A297270 1,1
%A A297270 _Clark Kimberling_, Jan 16 2018