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%I #4 Jan 16 2018 21:11:23
%S 11,22,23,33,34,35,44,45,46,47,55,56,57,58,59,66,67,68,69,70,71,77,78,
%T 79,80,81,82,83,88,89,90,91,92,93,94,95,99,100,101,102,103,104,105,
%U 106,107,110,111,112,113,114,115,116,117,118,119,121,132,143,154
%N Numbers whose base-11 digits have greater down-variation than up-variation; see Comments.
%C 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 Clark Kimberling, <a href="/A297273/b297273.txt">Table of n, a(n) for n = 1..10000</a>
%e 154 in base-11: 1,3,0, having DV = 3, UV = 2, so that 154 is in the sequence.
%t g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t b = 11; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t Take[Flatten[Position[w, -1]], 120] (* A297273 *)
%t Take[Flatten[Position[w, 0]], 120] (* A297274 *)
%t Take[Flatten[Position[w, 1]], 120] (* A297275 *)
%Y Cf. A297330, A297274, A297275.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 16 2018
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