A297254 - OEIS

%I #4 Jan 15 2018 21:07:45

%S 6,7,11,18,19,22,23,26,27,30,31,35,39,43,47,66,67,70,71,74,75,78,79,

%T 82,83,86,87,90,91,94,95,98,99,102,103,106,107,110,111,114,115,118,

%U 119,122,123,126,127,131,135,139,143,147,151,155,159,163,167,171,175

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

%C 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 Clark Kimberling, <a href="/A297254/b297254.txt">Table of n, a(n) for n = 1..10000</a>

%e 175 in base-4:  2,2,3,3, having DV = 0, UV = 1, so that 175 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 = 4; 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]   (* A297252 *)

%t Take[Flatten[Position[w, 0]], 120]    (* A297253 *)

%t Take[Flatten[Position[w, 1]], 120]    (* A297254 *)

%Y Cf. A297330, A297252, A297253.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 15 2018