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A292263 a(n) = A292264(A243071(n)). 7
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, 44, 767, 16, 1535, 16, 44, 190, 17, 16, 3071, 382, 92, 40, 6143, 40, 12287, 92, 16, 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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

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.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2048

FORMULA

a(n) = A292264(A243071(n)).

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

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.

a(n) = A292941(n) + A292945(n).

a(n) = A292253(n) + A292255(n).

PROG

(Scheme, two implementations)

(definec (A292263 n) (if (<= n 2) (- n 1) (+ (floor->exact (* (A000035 n) (/ (+ 1 (modulo n 3)) 2))) (* 2 (A292263 (A252463 n))))))

(definec (A292263 n) (if (<= n 2) (- n 1) (+ (* (A000035 n) (abs (jacobi-symbol 3 n))) (* 2 (A292263 (A252463 n))))))

CROSSREFS

Cf. A005940, A292253, A292255, A292941, A292945.

Sequence in context: A319925 A112472 A240412 * A238624 A124506 A264687

Adjacent sequences:  A292260 A292261 A292262 * A292264 A292265 A292266

KEYWORD

nonn

AUTHOR

Antti Karttunen, Sep 30 2017

STATUS

approved

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Last modified October 21 19:19 EDT 2019. Contains 328308 sequences. (Running on oeis4.)