

A292941


a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 6)].


8



0, 1, 2, 2, 4, 4, 9, 4, 4, 8, 18, 8, 37, 18, 8, 8, 74, 8, 149, 16, 16, 36, 298, 16, 9, 74, 8, 36, 596, 16, 1193, 16, 36, 148, 16, 16, 2387, 298, 72, 32, 4774, 32, 9549, 72, 16, 596, 19098, 32, 19, 18, 148, 148, 38196, 16, 33, 72, 296, 1192, 76392, 32, 152785, 2386, 32, 32, 72, 72, 305571, 296, 596, 32, 611142, 32, 1222285, 4774, 16, 596, 32
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OFFSET

1,3


COMMENTS

Base2 expansion of a(n) encodes the steps where numbers of the form 6k+1 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 bitposition towards right (less significant end).
The AND  XOR formulas just restate the fact that J(3n) = J(1n)*J(3n), as the Jacobisymbol is multiplicative (also) with respect to its upper argument.


LINKS



FORMULA

a(1) = 0, a(2) = 1, and for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 6)], where the last part of the formula is Iverson bracket, giving 1 only if n is of the form 6k+1, and 0 otherwise.
Also, for n > 2, a(n) = 2*a(A252463(n)) + [n == 1 (mod 2)]*[J(3n) = 1], where J is the Jacobisymbol.


PROG

(Scheme) (define (A292941 n) (if (<= n 2) ( n 1) (+ (if (= 1 (modulo n 6)) 1 0) (* 2 (A292941 (A252463 n))))))


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



