A297255 - OEIS

%I #4 Jan 15 2018 21:07:56

%S 5,10,11,15,16,17,20,21,22,23,25,30,35,40,45,50,51,55,56,60,61,65,66,

%T 70,71,75,76,77,80,81,82,85,86,87,90,91,92,95,96,97,100,101,102,103,

%U 105,106,107,108,110,111,112,113,115,116,117,118,120,121,122,123

%N Numbers whose base-5 digits have greater down-variation than up-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="/A297255/b297255.txt">Table of n, a(n) for n = 1..10000</a>

%e 123 in base-5:  4,4,3, having DV = 1, UV = 0, so that 123 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, A297256, A297257.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 15 2018