A292590 - OEIS

%I #13 Sep 23 2017 19:14:12

%S 0,0,1,2,0,5,10,2,21,42,4,85,0,0,171,342,10,5,684,20,1369,2738,4,5477,

%T 0,42,10955,8,84,21911,43822,8,21,87644,170,175289,350578,0,11,701156,

%U 0,1402313,40,342,2804627,16,684,85,5609254,20,11218509,22437018,10,44874037,89748074,1368,179496149,168,40,43,0,2738,1,358992298,5476,717984597,80,8

%N a(1) = 0; and for n > 1, a(n) = 2*a(A285712(n)) + [0 == (n mod 3)].

%C Binary expansion of a(n) encodes the positions of multiples of three in the path taken from n to the root in the binary trees like A245612 and A244154.

%H Antti Karttunen, <a href="/A292590/b292590.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>

%H <a href="/index/Pri#prime_indices">Index entries for sequences computed from indices in prime factorization</a>

%F a(1) = 0; and for n > 1, a(n) = A079978(n) + 2*a(A285712(n)).

%F a(n) + A292591(n) = A245611(n).

%F a(A245612(n)) = A292592(n).

%F A000120(a(n)) = A292594(n).

%t f[n_] := f[n] = Which[n == 1, 0, Mod[n, 3] == 2, Ceiling[n/3], True, (Times @@ Power[If[# == 1, 1, NextPrime[#, -1]] & /@ First@ #, Last@ #] &@ Transpose@ FactorInteger[2 n - 1] + 1)/2]; a[n_] := a[n] = If[n == 1, n - 1, 2 a[f@ n] + Boole[Divisible[n, 3]]]; Array[a, 67] (* _Michael De Vlieger_, Sep 22 2017 *)

%o (Scheme) (define (A292590 n) (if (<= n 1) 0 (+ (if (zero? (modulo n 3)) 1 0) (* 2 (A292590 (A285712 n))))))

%Y Cf. A079978, A244153, A245611, A285712, A292591, A292592, A292594.

%Y Cf. also A292244, A292383.

%K nonn

%O 1,4

%A _Antti Karttunen_, Sep 20 2017