%I
%S 5,10,11,15,16,17,20,21,22,23,25,30,35,40,45,50,51,55,56,60,61,65,66,
%T 70,71,75,76,77,80,81,82,85,86,87,90,91,92,95,96,97,100,101,102,103,
%U 105,106,107,108,110,111,112,113,115,116,117,118,120,121,122,123
%N Numbers whose base5 digits have greater downvariation than upvariation; see Comments.
%C Suppose that n has baseb digits b(m), b(m1), ..., b(0). The baseb downvariation of n is the sum DV(n,b) of all d(i)d(i1) for which d(i) > d(i1); the baseb upvariation of n is the sum UV(n,b) of all d(k1)d(k) for which d(k) < d(k1). The total baseb 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="/A297255/b297255.txt">Table of n, a(n) for n = 1..10000</a>
%e 123 in base5: 4,4,3, having DV = 1, UV = 0, so that 123 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 = 5; 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] (* A297255 *)
%t Take[Flatten[Position[w, 0]], 120] (* A297256 *)
%t Take[Flatten[Position[w, 1]], 120] (* A297257 *)
%Y Cf. A297330, A297256, A297257.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 15 2018
