|
%I #8 Jan 23 2018 20:38:35
%S 16,32,33,48,49,50,64,65,66,67,80,81,82,83,84,96,97,98,99,100,101,112,
%T 113,114,115,116,117,118,128,129,130,131,132,133,134,135,144,145,146,
%U 147,148,149,150,151,152,160,161,162,163,164,165,166,167,168,169
%N Numbers whose base-16 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 A296761 first at 288 = 120_16, which has the same number of rises and falls (so not in A296761) but DV =2 > UV =1 (so in this sequence). - _R. J. Mathar_, Jan 23 2018
%H Clark Kimberling, <a href="/A297288/b297288.txt">Table of n, a(n) for n = 1..10000</a>
%e 169 in base-16: 10,9 having DV = 1, UV = 0, so that 169 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 = 16; 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] (* A297288 *)
%t Take[Flatten[Position[w, 0]], 120] (* A297289 *)
%t Take[Flatten[Position[w, 1]], 120] (* A297290 *)
%Y Cf. A297330, A297289, A297290.
%K nonn,base,easy
%O 1,1
%A _Clark Kimberling_, Jan 17 2018
|
