cp's OEIS Frontend

A297254 Numbers whose base-4 digits have greater up-variation than down-variation; see Comments.

%I A297254 #4 Jan 15 2018 21:07:45
%S A297254 6,7,11,18,19,22,23,26,27,30,31,35,39,43,47,66,67,70,71,74,75,78,79,
%T A297254 82,83,86,87,90,91,94,95,98,99,102,103,106,107,110,111,114,115,118,
%U A297254 119,122,123,126,127,131,135,139,143,147,151,155,159,163,167,171,175
%N A297254 Numbers whose base-4 digits have greater up-variation than down-variation; see Comments.
%C A297254 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 A297254 Clark Kimberling, <a href="/A297254/b297254.txt">Table of n, a(n) for n = 1..10000</a>
%e A297254 175 in base-4:  2,2,3,3, having DV = 0, UV = 1, so that 175 is in the sequence.
%t A297254 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297254 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297254 b = 4; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297254 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297254 Take[Flatten[Position[w, -1]], 120]   (* A297252 *)
%t A297254 Take[Flatten[Position[w, 0]], 120]    (* A297253 *)
%t A297254 Take[Flatten[Position[w, 1]], 120]    (* A297254 *)
%Y A297254 Cf. A297330, A297252, A297253.
%K A297254 nonn,base,easy
%O A297254 1,1
%A A297254 _Clark Kimberling_, Jan 15 2018