A366347 a(n) has as many prime factors as the ternary expansion of n has runs of nonzero digits; if the k-th run corresponds to A032924(e) and appears after m-1 0's then the p-adic valuation of a(n) is e (where p corresponds to the m-th prime number).

1, 2, 4, 3, 8, 16, 9, 32, 64, 5, 6, 12, 27, 128, 256, 81, 512, 1024, 25, 18, 36, 243, 2048, 4096, 729, 8192, 16384, 7, 10, 20, 15, 24, 48, 45, 96, 192, 125, 54, 108, 2187, 32768, 65536, 6561, 131072, 262144, 625, 162, 324, 19683, 524288, 1048576, 59049

Offset

0,2

Comments

This sequence is a variant of the Doudna sequence (A005940); here we consider runs of nonzero digits in ternary expansions, there in binary expansions.

This sequence is a bijection from the nonnegative integers to the positive integers with inverse A366348.

We can devise a similar sequence for any fixed base b >= 2:

- the case b = 2 corresponds (up to the offset) to the Doudna sequence (A005940),

- the case b = 3 corresponds to the present sequence,

- the case b = 10 corresponds to A290389.

Links

Table of n, a(n) for n=0..51.

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

a(3*n) = A003961(a(n)).

a(3^k) = prime(1 + k) for any k >= 0.

a(2 * 3^k) = prime(1 + k)^2 for any k >= 0.

a(n) is squarefree iff n belongs to A060140.

Example

For n = 46: the ternary expansion of 46 is "1201; we have two runs of nonzero digits: "12" (= 5 = A032924(4)) after 2-1 0's and "1" (= 1 = A032924(1)) after 1-1 0's; so a(46) = prime(2)^4 * prime(1)^1 = 3^4 * 2^1 = 162.

Prog

(PARI) See Links section.

Crossrefs

Cf. A003961, A005940, A032924, A060140, A290389, A365278, A366348 (inverse).

Sequence in context: A193949 A246679 A244153 * A308328 A277415 A243051

Adjacent sequences: A366344 A366345 A366346 * A366348 A366349 A366350

Keyword

nonn,base

Author

Rémy Sigrist, Oct 07 2023

Status

approved