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A293445 A multiplicative encoding (base-2 compressed) for the exponents of 3 obtained when using Shevelev's algorithm for computing A053446. 3
2, 2, 3, 12, 36, 3, 12, 24, 6, 48, 12, 20736, 82944, 12, 18, 864, 248832, 6, 20, 19906560, 59719680, 80, 8640, 720, 25920, 34560, 5, 80, 103195607040, 240, 480, 622080, 137594142720, 138240, 20, 59440669655040, 138240, 20, 14929920, 29859840, 240, 59719680, 8640, 720, 414720, 8640, 540, 447897600, 960, 46080, 34560, 59719680, 295814814232058265600, 5, 80 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..1458

FORMULA

A048675(a(n)) = A053446(n).

EXAMPLE

A001651(5) = 7 as 7 is the fifth number not divisible by 3. According to the algorithm described in the comment of A053446 we have in the form of a "finite continued fraction"

    1 + 14

    ------ + 7

       3^1

    ---------- + 14

          3^1

    ----------------- + 7

            3^2

    ---------------------- = 1

               3^2

Cumulatively multiplying (with A019565) together the prime-numbers corresponding to 1-bits in the binary expansions of the exponents of 3 in the denominators (that are 1, 1, 2, 2, in binary 1, 1, 10, 10, with 1's in bit-positions 0 and 1), yields prime(0+1) * prime(0+1) * prime(1+1) * prime(1+1) = 2^2 * 3^2 = 36, thus a(5) = 36.

(Adapted from Vladimir Shevelev's explanation in A053446.)

Another example: A001651(19) = 28 as 28 is the 19th number not divisible by 3. (1 + 28) is not a multiple of 3, so we start with (1 + 2*28) = 1+56 = 57 and proceed as:

    1 + 56

    ------ + 56                     [that is, (57/3) + 56 = 75]

       3^1

    ---------- + 56                 [that is, (75/3) + 56 = 81]

          3^1

    -----------------  = 1          [that is, (81/81) = 1]

            3^4

So we obtained exponents 1, 1, 4 (in binary "1", "1" and "100") where the 1-bits are in positions 0, 0 and 2. We form a product prime(0+1) * prime(0+1) * prime(2+1) = 2*2*5, thus a(19) = 20.

PROG

(Scheme)

(define (A293445 n) (define (next_one k m) (if (zero? (modulo (+ k m) 3)) (+ k m) (+ k m m))) (let* ((u (A001651 n)) (x_init (next_one 1 u))) (let loop ((x x_init) (z (A019565 (A007949 x_init)))) (let ((r (A038502 x))) (if (= 1 r) z (let ((x_next (next_one r u))) (loop x_next (* z (A019565 (A007949 x_next))))))))))

(define (A001651 n) (let ((x (- n 1))) (if (even? x) (+ 1 (* 3 (/ x 2))) (- (* 3 (/ (+ x 1) 2)) 1))))

(define (A038500 n) (A000244 (A007949 n)))

(define (A038502 n) (/ n (A038500 n)))

CROSSREFS

Cf. A001651, A007949, A019565, A038502, A053446, A293220.

Cf. A293446 (restricted growth transform of this sequence).

Cf. also A292265.

Sequence in context: A182779 A199673 A240133 * A126339 A268725 A153929

Adjacent sequences:  A293442 A293443 A293444 * A293446 A293447 A293448

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 09 2017

STATUS

approved

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Last modified June 17 14:09 EDT 2019. Contains 324185 sequences. (Running on oeis4.)