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A297278 Numbers whose base-12 digits have greater up-variation than down-variation; see Comments.

%I A297278 #4 Jan 17 2018 09:43:25
%S A297278 14,15,16,17,18,19,20,21,22,23,27,28,29,30,31,32,33,34,35,40,41,42,43,
%T A297278 44,45,46,47,53,54,55,56,57,58,59,66,67,68,69,70,71,79,80,81,82,83,92,
%U A297278 93,94,95,105,106,107,118,119,131,146,147,148,149,150,151
%N A297278 Numbers whose base-12 digits have greater up-variation than down-variation; see Comments.
%C A297278 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 A297278 Clark Kimberling, <a href="/A297278/b297278.txt">Table of n, a(n) for n = 1..10000</a>
%e A297278 151 in base-12:  1,0,7, having DV = 1, UV = 7, so that 151 is in the sequence.
%t A297278 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297278 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297278 b = 12; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297278 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297278 Take[Flatten[Position[w, -1]], 120]   (* A297276 *)
%t A297278 Take[Flatten[Position[w, 0]], 120]    (* A297277 *)
%t A297278 Take[Flatten[Position[w, 1]], 120]    (* A297278 *)
%Y A297278 Cf. A297330, A297276, A297277.
%K A297278 nonn,base,easy
%O A297278 1,1
%A A297278 _Clark Kimberling_, Jan 17 2018