A292385 - OEIS

%I #12 Sep 18 2017 09:27:18

%S 0,1,2,2,5,4,10,4,5,10,20,8,41,20,8,8,83,10,166,20,21,40,332,16,11,82,

%T 8,40,665,16,1330,16,41,166,16,20,2661,332,80,40,5323,42,10646,80,17,

%U 664,21292,32,23,22,164,164,42585,16,42,80,333,1330,85170,32,170341,2660,40,32,83,82,340682,332,665,32,681364,40,1362729,5322,20,664,33,160

%N a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 4)].

%C Variant of A292381. Here the most significant 1-bit is at the one step smaller position.

%H Antti Karttunen, <a href="/A292385/b292385.txt">Table of n, a(n) for n = 1..2048</a>

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

%F a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 4)], where the last part of the formula is Iverson bracket, giving 1 only if n is of the form 4k+1, and 0 otherwise.

%F For n >= 1, a(n) + A292383(n) = A243071(n); a(A163511(n)) = A292271(n).

%F For n >= 2, A004754(a(n)) = A292381(n).

%o (Scheme, with memoization-macro definec)

%o (definec (A292385 n) (if (<= n 2) (- n 1) (+ (if (= 1 (modulo n 4)) 1 0) (* 2 (A292385 (A252463 n))))))

%Y Cf. A004754, A163511, A243071, A252463, A292381, A292383.

%K nonn,base

%O 1,3

%A _Antti Karttunen_, Sep 16 2017