A297276 - OEIS

%I #8 Jan 23 2018 19:54:02

%S 12,24,25,36,37,38,48,49,50,51,60,61,62,63,64,72,73,74,75,76,77,84,85,

%T 86,87,88,89,90,96,97,98,99,100,101,102,103,108,109,110,111,112,113,

%U 114,115,116,120,121,122,123,124,125,126,127,128,129,132,133,134

%N Numbers whose base-12 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.

%C Differs from A296749 first at 168 = 120_12, which is in not in A296749 because it has the same number of rises and falls, but in here because DV(168,12) =2 > UV(168,12) =1. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297276/b297276.txt">Table of n, a(n) for n = 1..10000</a>

%e 134 in base-12:  11,2, having DV = 9, UV = 0, so that 134 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 = 12; 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]   (* A297276 *)

%t Take[Flatten[Position[w, 0]], 120]    (* A297277 *)

%t Take[Flatten[Position[w, 1]], 120]    (* A297278 *)

%Y Cf. A297330, A297277, A297278.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 16 2018