A227413 a(1)=1, a(2n)=nthprime(a(n)), a(2n+1)=nthcomposite(a(n)), where nthprime = A000040, nthcomposite = A002808.

1, 2, 4, 3, 6, 7, 9, 5, 8, 13, 12, 17, 14, 23, 16, 11, 10, 19, 15, 41, 22, 37, 21, 59, 27, 43, 24, 83, 35, 53, 26, 31, 20, 29, 18, 67, 30, 47, 25, 179, 58, 79, 34, 157, 54, 73, 33, 277, 82, 103, 40, 191, 62, 89, 36, 431, 114, 149, 51, 241, 75, 101, 39, 127, 46

Offset

1,2

Comments

Inverse permutation of A135141.

Shares with A073846 the property that the other bisection consists of just primes and the other bisection of just nonprimes.

Links

Antti Karttunen and Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Index entries for sequences that are permutations of the natural numbers

Formula

a(1)=1, a(2n) = A000040(a(n)), a(2n+1) = A002808(a(n)).

A007097(n) = a(A000079(n)).

Prog

(Scheme, with Antti Karttunen's IntSeq-library)
(definec (A227413 n) (cond ((< n 2) n) ((even? n) (A000040 (A227413 (/ n 2)))) (else (A002808 (A227413 (/ (- n 1) 2))))))
(Haskell)
import Data.List (transpose)
a227413 n = a227413_list !! (n-1)
a227413_list = 1 : concat (transpose [map a000040 a227413_list,
                                      map a002808 a227413_list])
-- Reinhard Zumkeller, Jan 29 2014

Crossrefs

Similarly constructed permutations: A227402, A227404, A227410, A227412. Cf. also A073846, A209636.

Sequence in context: A367262 A358467 A006016 * A217122 A239622 A245604

Adjacent sequences: A227410 A227411 A227412 * A227414 A227415 A227416

Keyword

nonn,look

Author

Antti Karttunen, Jul 10 2013

Status

approved