A322016 - OEIS

%I #13 Jan 28 2021 11:33:24

%S 0,0,1,0,3,4,0,0,7,8,9,0,0,12,0,0,15,16,17,0,19,20,0,0,0,24,25,0,0,28,

%T 0,0,31,32,33,0,35,36,0,0,39,40,41,0,0,44,0,0,0,48,49,0,51,52,0,0,0,

%U 56,57,0,0,60,0,0,63,64,65,0,67,68,0,0,71,72,73,0,0,76,0,0,79,80,81,0,83,84,0,0,0,88,89,0,0,92,0,0,0,96,97

%N a(0) = 0; for n > 0, if A003188(n) > A003188(n-1) then a(n) = n-1, otherwise a(n) = 0.

%H Antti Karttunen, <a href="/A322016/b322016.txt">Table of n, a(n) for n = 0..16383</a>

%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>

%F a(0) = 0; for n > 0, a(n) = (1/2)*(A034947(n)+1)*(n-1).

%t With[{nn = 98}, {0, 0}~Join~Most@ ReplacePart[ConstantArray[0, nn], Map[# -> # &, Position[Partition[Array[BitXor[#, Floor[#/2]] &, nn], 2, 1], _?(First@ # < Last@ # &), {1}, Heads -> False][[All, 1]] ]]] (* _Michael De Vlieger_, Nov 25 2018 *)

%t Join[{0,0},With[{t=Partition[Table[BitXor[n,Floor[n/2]],{n,100}],2,1]},Flatten[ If[#[[1]]<#[[2]],Position[t,#],0]&/@t]]] (* _Harvey P. Dale_, Jan 28 2021 *)

%o (PARI)

%o A003188(n) = bitxor(n, n>>1);

%o A322016(n) = if(0==n,0,if(A003188(n)>A003188(n-1),n-1,0));

%o (PARI) A322016(n) = if(!n,0,(((kronecker(-1,n)+1)/2)*(n-1)));

%Y Cf. A003188, A034947, A322015, A322017.

%K nonn

%O 0,5

%A _Antti Karttunen_, Nov 24 2018