A297285 - OEIS

%I #8 Jan 23 2018 20:16:43

%S 15,30,31,45,46,47,60,61,62,63,75,76,77,78,79,90,91,92,93,94,95,105,

%T 106,107,108,109,110,111,120,121,122,123,124,125,126,127,135,136,137,

%U 138,139,140,141,142,143,150,151,152,153,154,155,156,157,158,159,165

%N Numbers whose base-15 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 A296758 first for 255 = 120_15, which has the same number of rises and falls and is not in A296758, but DV(255,15) =2 > UV(255,15) =1 and is in this sequence. - _R. J. Mathar_, Jan 23 2018

%H Clark Kimberling, <a href="/A297285/b297285.txt">Table of n, a(n) for n = 1..10000</a>

%e 165 in base-15:  11,0 having DV = 11, UV = 0, so that 165 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 = 15; 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]   (* A297285 *)

%t Take[Flatten[Position[w, 0]], 120]    (* A297286 *)

%t Take[Flatten[Position[w, 1]], 120]    (* A297287 *)

%Y Cf. A297330, A297286, A297287.

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_, Jan 17 2018