|
%I #7 Sep 30 2017 16:06:36
%S 0,0,0,0,1,0,3,0,0,2,6,0,12,6,0,0,25,0,51,4,4,12,102,0,0,24,0,12,205,
%T 0,411,0,12,50,0,0,822,102,24,8,1645,8,3291,24,0,204,6582,0,0,0,48,48,
%U 13165,0,9,24,100,410,26330,0,52660,822,8,0,25,24,105321,100,204,0,210642,0,421284,1644,0,204,1,48,842569,16,0,3290,1685138,16,48,6582
%N a(1) = 0, and for n > 1, a(n) = 2*a(A252463(n)) + [n == 1 (mod 2)]*[J(3|n) == -1], where J is the Jacobi-symbol.
%C Base-2 expansion of a(n) encodes the steps where numbers that are either of the form 12k+5 or of the form 12k+7 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n.
%C The AND - XOR formulas just restate the fact that J(3|n) = J(-1|n)*J(-3|n), as the Jacobi-symbol is multiplicative (also) with respect to its upper argument.
%H Antti Karttunen, <a href="/A292255/b292255.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) = 2*a(A252463(n)) + [n == 1 (mod 2)]*[J(3|n) == -1], where J is the Jacobi-symbol, and [ ]'s are Iverson brackets, whose product gives 1 only if n is an odd number for which J(3|n) = -1, and 0 otherwise.
%F a(n) = A292263(n) AND (A292383(n) XOR A292945(n)), where AND is bitwise-and (A004198) and XOR is bitwise-XOR (A003987).
%F a(n) = A292263(n) AND (A292385(n) XOR A292941(n)). [See comments.]
%F For n >= 0, a(A163511(n)) = A292256(n).
%F For n >= 1, a(n) + A292253(n) + A292943(n) = A243071(n).
%o (Scheme) (define (A292255 n) (if (<= n 1) 0 (+ (if (and (odd? n) (= -1 (jacobi-symbol 3 n))) 1 0) (* 2 (A292255 (A252463 n))))))
%Y Cf. A005940, A163511, A243071, A292253, A292256, A292263, A292943.
%Y Cf. also A292941, A292945.
%K nonn
%O 1,7
%A _Antti Karttunen_, Sep 28 2017
|
