cp's OEIS Frontend

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

%I A227413 #19 Jan 29 2014 17:20:44
%S A227413 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,
%T A227413 24,83,35,53,26,31,20,29,18,67,30,47,25,179,58,79,34,157,54,73,33,277,
%U A227413 82,103,40,191,62,89,36,431,114,149,51,241,75,101,39,127,46
%N A227413 a(1)=1, a(2n)=nthprime(a(n)), a(2n+1)=nthcomposite(a(n)), where nthprime = A000040, nthcomposite = A002808.
%C A227413 Inverse permutation of A135141.
%C A227413 Shares with A073846 the property that the other bisection consists of just primes and the other bisection of just nonprimes.
%H A227413 Antti Karttunen and Reinhard Zumkeller, <a href="/A227413/b227413.txt">Table of n, a(n) for n = 1..1000</a>
%H A227413 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A227413 a(1)=1, a(2n) = A000040(a(n)), a(2n+1) = A002808(a(n)).
%F A227413 A007097(n) = a(A000079(n)).
%o A227413 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A227413 (definec (A227413 n) (cond ((< n 2) n) ((even? n) (A000040 (A227413 (/ n 2)))) (else (A002808 (A227413 (/ (- n 1) 2))))))
%o A227413 (Haskell)
%o A227413 import Data.List (transpose)
%o A227413 a227413 n = a227413_list !! (n-1)
%o A227413 a227413_list = 1 : concat (transpose [map a000040 a227413_list,
%o A227413                                       map a002808 a227413_list])
%o A227413 -- _Reinhard Zumkeller_, Jan 29 2014
%Y A227413 Similarly constructed permutations: A227402, A227404, A227410, A227412. Cf. also A073846, A209636.
%K A227413 nonn,look
%O A227413 1,2
%A A227413 _Antti Karttunen_, Jul 10 2013