A245603 Permutation of natural numbers: a(1) = 1; thereafter, if n is k-th number with an odd number of prime divisors (counted with multiplicity) [i.e., n = A026424(k)], a(n) = 2*a(k), otherwise, when n is k-th number > 1 with an even number of prime divisors [i.e., n = A028260(1+k)], a(n) = 1+(2*a(k)).

1, 2, 4, 3, 8, 5, 6, 16, 9, 7, 10, 12, 32, 17, 11, 13, 18, 14, 20, 24, 33, 19, 64, 15, 21, 25, 34, 22, 26, 36, 28, 40, 65, 35, 23, 27, 48, 37, 29, 41, 66, 38, 128, 30, 42, 49, 50, 68, 67, 44, 39, 52, 72, 129, 31, 43, 51, 69, 56, 45, 80, 53, 130, 73, 57, 70, 46, 54, 81, 96, 74, 58, 82, 131, 132, 76, 71, 256, 60

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, and for n > 1, if A066829(n) = 1, then a(n) = 2 * A245603(A055038(n)), otherwise a(n) = 1 + (2 * A245603(A055037(n)-1)).

As a composition of related permutations:

a(n) = A244321(A245613(n)).

For all n >= 1, A000035(a(n)) = 1 - A066829(n). [Permutation A143692 has the same property.]

Prog

(Scheme, with memoization macro definec)
(definec (A245603 n) (cond ((= 1 n) 1) ((= 1 (A066829 n)) (* 2 (A245603 (A055038 n)))) (else (+ 1 (* 2 (A245603 (-1+ (A055037 n))))))))

Crossrefs

Inverse: A245604.

Cf. A026424, A028260, A066829, A055037, A055038.

Similar permutations: A143692, A244152, A244321, A245613, A245605, A245607.

Sequence in context: A098709 A054238 A225589 * A371591 A048679 A342794

Adjacent sequences: A245600 A245601 A245602 * A245604 A245605 A245606

Keyword

nonn

Author

Antti Karttunen, Jul 27 2014

Status

approved