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A297284 Numbers whose base-14 digits have greater up-variation than down-variation; see Comments.

%I A297284 #9 Jan 23 2018 20:14:07
%S A297284 16,17,18,19,20,21,22,23,24,25,26,27,31,32,33,34,35,36,37,38,39,40,41,
%T A297284 46,47,48,49,50,51,52,53,54,55,61,62,63,64,65,66,67,68,69,76,77,78,79,
%U A297284 80,81,82,83,91,92,93,94,95,96,97,106,107,108,109,110,111
%N A297284 Numbers whose base-14 digits have greater up-variation than down-variation; see Comments.
%C A297284 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 A297284 Differs from A296754 first at 198 =102_14, which is in this sequence because UV(102,14) = 2 > DV(102,14) =1, but has the same number of rises and falls and is not in A296754. - _R. J. Mathar_, Jan 23 2018
%H A297284 Clark Kimberling, <a href="/A297284/b297284.txt">Table of n, a(n) for n = 1..10000</a>
%e A297284 111 in base-14:  7,13 having DV = 0, UV = 6, so that 111 is in the sequence.
%t A297284 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297284 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297284 b = 14; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297284 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297284 Take[Flatten[Position[w, -1]], 120]   (* A297282 *)
%t A297284 Take[Flatten[Position[w, 0]], 120]    (* A297283 *)
%t A297284 Take[Flatten[Position[w, 1]], 120]    (* A297284 *)
%Y A297284 Cf. A297330, A297282, A297283.
%K A297284 nonn,base,easy
%O A297284 1,1
%A A297284 _Clark Kimberling_, Jan 17 2018