%I
%S 7,8,9,13,14,19,27,28,29,32,33,34,37,38,39,42,43,44,47,48,49,53,54,58,
%T 59,63,64,68,69,73,74,79,84,89,94,99,127,128,129,132,133,134,137,138,
%U 139,142,143,144,147,148,149,152,153,154,157,158,159,162,163
%N Numbers whose base5 digits have greater upvariation than downvariation; 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="/A297257/b297257.txt">Table of n, a(n) for n = 1..10000</a>
%e 163 in base5: 1,1,2,3, having DV = 0, UV = 2, so that 163 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, A297255, A297256.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 15 2018
