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A297279 Numbers whose base-13 digits have greater down-variation than up-variation; see Comments.

%I A297279 #9 Jan 23 2018 20:00:02
%S A297279 13,26,27,39,40,41,52,53,54,55,65,66,67,68,69,78,79,80,81,82,83,91,92,
%T A297279 93,94,95,96,97,104,105,106,107,108,109,110,111,117,118,119,120,121,
%U A297279 122,123,124,125,130,131,132,133,134,135,136,137,138,139,143,144
%N A297279 Numbers whose base-13 digits have greater down-variation than up-variation; see Comments.
%C A297279 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 A297279 Differs from A296752 first for 195 = 120_13, which has the same number of rises and falls and is therefore not in A296752, but has DV(195,13) =2 > UV(195,13) = 1 and is in this sequence. - _R. J. Mathar_, Jan 23 2018
%H A297279 Clark Kimberling, <a href="/A297279/b297279.txt">Table of n, a(n) for n = 1..10000</a>
%e A297279 144 in base-13:  11,1, having DV = 10, UV = 0, so that 144 is in the sequence.
%t A297279 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297279 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297279 b = 13; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297279 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297279 Take[Flatten[Position[w, -1]], 120]   (* A297279 *)
%t A297279 Take[Flatten[Position[w, 0]], 120]    (* A297280 *)
%t A297279 Take[Flatten[Position[w, 1]], 120]    (* A297281 *)
%Y A297279 Cf. A297330, A297280, A297281.
%K A297279 nonn,base,easy
%O A297279 1,1
%A A297279 _Clark Kimberling_, Jan 17 2018