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A297255 Numbers whose base-5 digits have greater down-variation than up-variation; see Comments.

%I A297255 #4 Jan 15 2018 21:07:56
%S A297255 5,10,11,15,16,17,20,21,22,23,25,30,35,40,45,50,51,55,56,60,61,65,66,
%T A297255 70,71,75,76,77,80,81,82,85,86,87,90,91,92,95,96,97,100,101,102,103,
%U A297255 105,106,107,108,110,111,112,113,115,116,117,118,120,121,122,123
%N A297255 Numbers whose base-5 digits have greater down-variation than up-variation; see Comments.
%C A297255 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 A297255 Clark Kimberling, <a href="/A297255/b297255.txt">Table of n, a(n) for n = 1..10000</a>
%e A297255 123 in base-5:  4,4,3, having DV = 1, UV = 0, so that 123 is in the sequence.
%t A297255 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297255 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297255 b = 5; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297255 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297255 Take[Flatten[Position[w, -1]], 120]   (* A297255 *)
%t A297255 Take[Flatten[Position[w, 0]], 120]    (* A297256 *)
%t A297255 Take[Flatten[Position[w, 1]], 120]    (* A297257 *)
%Y A297255 Cf. A297330, A297256, A297257.
%K A297255 nonn,base,easy
%O A297255 1,1
%A A297255 _Clark Kimberling_, Jan 15 2018