OFFSET
1,3
COMMENTS
Base-2 expansion of a(n) encodes the steps where numbers that are either of the form 12k+1 or of the form 12k+11 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.
The AND - XOR formula(s) 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.
LINKS
FORMULA
a(1) = 0, a(2) = 1, and for n > 2, 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.
PROG
CROSSREFS
KEYWORD
nonn
AUTHOR
Antti Karttunen, Sep 28 2017
STATUS
approved