cp's OEIS Frontend

A297260 Numbers whose base-6 digits have greater up-variation than down-variation; see Comments.

%I A297260 #4 Jan 15 2018 21:08:35
%S A297260 8,9,10,11,15,16,17,22,23,29,38,39,40,41,44,45,46,47,50,51,52,53,56,
%T A297260 57,58,59,62,63,64,65,68,69,70,71,75,76,77,81,82,83,87,88,89,93,94,95,
%U A297260 99,100,101,105,106,107,112,113,118,119,124,125,130,131,136
%N A297260 Numbers whose base-6 digits have greater up-variation than down-variation; see Comments.
%C A297260 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 A297260 Clark Kimberling, <a href="/A297260/b297260.txt">Table of n, a(n) for n = 1..10000</a>
%e A297260 136 in base-6:  3,4,4, having DV = 0, UV = 1, so that 136 is in the sequence.
%t A297260 g[n_, b_] := Map[Total, GatherBy[Differences[IntegerDigits[n, b]], Sign]];
%t A297260 x[n_, b_] := Select[g[n, b], # < 0 &]; y[n_, b_] := Select[g[n, b], # > 0 &];
%t A297260 b = 6; z = 2000; p = Table[x[n, b], {n, 1, z}]; q = Table[y[n, b], {n, 1, z}];
%t A297260 w = Sign[Flatten[p /. {} -> {0}] + Flatten[q /. {} -> {0}]];
%t A297260 Take[Flatten[Position[w, -1]], 120]   (* A297258 *)
%t A297260 Take[Flatten[Position[w, 0]], 120]    (* A297259 *)
%t A297260 Take[Flatten[Position[w, 1]], 120]    (* A297260 *)
%Y A297260 Cf. A297330, A297258, A297259.
%K A297260 nonn,base,easy
%O A297260 1,1
%A A297260 _Clark Kimberling_, Jan 15 2018