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A297275 Numbers whose base-11 digits have greater up-variation than down-variation; see Comments.

%I A297275 #4 Jan 16 2018 21:11:35
%S A297275 13,14,15,16,17,18,19,20,21,25,26,27,28,29,30,31,32,37,38,39,40,41,42,
%T A297275 43,49,50,51,52,53,54,61,62,63,64,65,73,74,75,76,85,86,87,97,98,109,
%U A297275 123,124,125,126,127,128,129,130,131,134,135,136,137,138,139
%N A297275 Numbers whose base-11 digits have greater up-variation than down-variation; see Comments.
%C A297275 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 A297275 Clark Kimberling, <a href="/A297275/b297275.txt">Table of n, a(n) for n = 1..10000</a>
%e A297275 139 in base-11:  1,1,7, having DV = 0, UV = 6, so that 139 is in the sequence.
%t A297275 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297275 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297275 b = 11; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297275 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297275 Take[Flatten[Position[w, -1]], 120]   (* A297273 *)
%t A297275 Take[Flatten[Position[w, 0]], 120]    (* A297274 *)
%t A297275 Take[Flatten[Position[w, 1]], 120]    (* A297275 *)
%Y A297275 Cf. A297330, A297273, A297274.
%K A297275 nonn,base,easy
%O A297275 1,1
%A A297275 _Clark Kimberling_, Jan 16 2018