A372744 If the n-th 3-smooth number, A003586(n), equals 2^i * 3^j for some i, j >= 0, then the a(n)-th 3-smooth number, A003586(a(n)), equals 2^j * 3^i.

1, 3, 2, 7, 5, 12, 4, 10, 19, 8, 16, 6, 27, 14, 24, 11, 37, 21, 9, 33, 18, 49, 30, 15, 44, 26, 13, 62, 40, 23, 57, 36, 20, 77, 52, 32, 17, 71, 47, 29, 93, 66, 43, 25, 87, 60, 39, 111, 22, 81, 55, 35, 104, 75, 51, 131, 31, 98, 69, 46, 123, 28, 91, 64, 152, 42

Offset

1,2

Comments

This sequence is a self-inverse permutation of the positive integers with infinitely many fixed points (A202821).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Rémy Sigrist, PARI program

Index entries for sequences that are permutations of the natural numbers

Formula

A022328(a(n)) = A022329(n).

A022329(a(n)) = A022328(n).

a(n) = n iff n belongs to A202821.

sign(a(n) - n) = sign(A022328(n) - A022329(n)).

Example

A003586(8) = 12 = 2^2 * 3^1, A003586(10) = 18 = 2^1 * 3^2, so a(8) = 10 and.

Prog

(PARI) \\ See Links section.

Crossrefs

Cf. A003586, A022328, A022329, A202821 (fixed points).

Sequence in context: A130922 A353170 A263018 * A215622 A195820 A006921

Adjacent sequences: A372741 A372742 A372743 * A372745 A372746 A372747

Keyword

nonn

Author

Rémy Sigrist, May 12 2024

Status

approved