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%I #7 Sep 30 2017 16:06:50
%S 0,1,2,2,5,4,11,4,4,10,23,8,47,22,8,8,95,8,191,20,20,46,383,16,9,94,8,
%T 44,767,16,1535,16,44,190,17,16,3071,382,92,40,6143,40,12287,92,16,
%U 766,24575,32,19,18,188,188,49151,16,41,88,380,1534,98303,32,196607,3070,40,32,89,88,393215,380,764,34,786431,32,1572863,6142,16,764
%N a(n) = A292264(A243071(n)).
%C Base-2 expansion of a(n) encodes the steps where numbers that are neither multiples of 2 nor 3 are encountered when map x -> A252463(x) is iterated down to 1, starting from x=n. An exception is the most significant bit of a(n) which corresponds with the final 1, but is shifted one bit-position towards right.
%H Antti Karttunen, <a href="/A292263/b292263.txt">Table of n, a(n) for n = 1..2048</a>
%F a(n) = A292264(A243071(n)).
%F a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n = -1 or +1 (mod 6)].
%F Also, for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 2)]*[abs(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 or -1, and 0 otherwise.
%F a(n) = A292941(n) + A292945(n).
%F a(n) = A292253(n) + A292255(n).
%o (Scheme, two implementations)
%o (definec (A292263 n) (if (<= n 2) (- n 1) (+ (floor->exact (* (A000035 n) (/ (+ 1 (modulo n 3)) 2))) (* 2 (A292263 (A252463 n))))))
%o (definec (A292263 n) (if (<= n 2) (- n 1) (+ (* (A000035 n) (abs (jacobi-symbol 3 n))) (* 2 (A292263 (A252463 n))))))
%Y Cf. A005940, A292253, A292255, A292941, A292945.
%K nonn
%O 1,3
%A _Antti Karttunen_, Sep 30 2017
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