A143692 -id:A143692 - cp's OEIS frontend

A143694 A143692(A143692(n)).

1, 2, 3, 4, 5, 6, 10, 9, 8, 7, 14, 11, 15, 12, 16, 13, 20, 24, 19, 21, 18, 22, 25, 17, 26, 23, 30, 34, 38, 29, 33, 35, 28, 32, 36, 27, 39, 31, 40, 37, 44, 48, 41, 54, 56, 42, 58, 47, 46, 51, 50, 55, 57, 52, 43, 45, 60, 49, 59, 53, 61, 62, 68, 64, 66, 72, 74, 78, 63, 67, 84, 86

Offset: 1

Reinhard Zumkeller, Aug 29 2008

nonn

Permutation of the natural numbers with inverse A143693.

Indexentries for sequences that are permutations of the natural numbers

A143691.

A143691 Lexicographically earliest permutation of the natural numbers having alternating even and odd numbers of prime factors.

Original entry on oeis.org

1, 2, 4, 3, 6, 5, 9, 7, 10, 8, 14, 11, 15, 12, 16, 13, 21, 17, 22, 18, 24, 19, 25, 20, 26, 23, 33, 27, 34, 28, 35, 29, 36, 30, 38, 31, 39, 32, 40, 37, 46, 41, 49, 42, 51, 43, 54, 44, 55, 45, 56, 47, 57, 48, 58, 50, 60, 52, 62, 53, 64, 59, 65, 61, 69, 63, 74, 66, 77, 67, 81, 68

Offset: 1

Reinhard Zumkeller, Aug 29 2008

nonn

A066829(a(n)*a(n+1)) = 1; n mod 2 + A001222(a(n)) = 1;
a(2*n) = A026424(n); a(2*n-1) = A028260(n);
a(a(n)) = A143693(n).

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for sequences that are permutations of the natural numbers

Cf. A143692 (inverse), A001222, A066829, A026424, A028260, A143693, A109465.

import Data.List (delete)
a143691 n = a143691_list !! (n-1)
a143691_list = f 1 [1..] where
   f m xs = g xs where
     g (z:zs) = if m + m' /= 1 then g zs else z : f m' (delete z xs)
                where m' = a001222 z `mod` 2
-- Reinhard Zumkeller, Aug 07 2014

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) = 2a(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+(2a(k)).

Original entry on oeis.org

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

Antti Karttunen, Jul 27 2014

nonn

Antti Karttunen, Table of n, a(n) for n = 1..10001
Index entries for sequences that are permutations of the natural numbers

Inverse: A245604.
Cf. A026424, A028260, A066829, A055037, A055038.
Similar permutations: A143692, A244152, A244321, A245613, A245605, A245607.

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.]

cp's OEIS Frontend

A143694 A143692(A143692(n)).

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A143691 Lexicographically earliest permutation of the natural numbers having alternating even and odd numbers of prime factors.

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Haskell

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