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%I #10 Mar 23 2014 01:43:32
%S 1,1,2,1,3,2,5,1,7,3,11,2,13,5,17,1,19,7,23,3,29,11,31,2,37,13,41,5,
%T 43,17,47,1,53,19,59,7,61,23,67,3,71,29,73,11,79,31,83,2,89,37,97,13,
%U 101,41,103,5,107,43,109,17,113,47,127,1,131,53,137,19,139,59,149,7,151,61
%N 1 followed by the primes, interleaved recursively.
%C a(2*n-1) = A008578(n); a(2*n+1) = A000040(n);
%C a((2*n-1)*2^k) = A008578(n), k >= 0;
%C a(2^k) = 1, k >= 0; a(2^k - 1) = A051438(k), k > 0.
%H R. Zumkeller, <a href="/A181363/b181363.txt">Table of n, a(n) for n = 1..8191</a>
%F a(n) = if even n then a(n/2) else A008578((n+1)/2).
%F a(n) = A008578(A025480(n-1)+1). - _Reinhard Zumkeller_, Mar 22 2014
%e Initial values, seen as a binary tree:
%e ................................. 1
%e ................ 1 _______________________________ 2
%e ........ 1 _____________ 3 .............. 2 ______________ 5
%e ... 1 _____ 7 ..... 3 ______ 11 .... 2 ______ 13 .... 5 ______ 17
%e .. 1__19...7__23...3__29...11__31...2__37...13__41...5__43...17__47
%o (Haskell)
%o import Data.List (transpose)
%o a181363 n = a181363_list !! (n-1)
%o a181363_list = concat $ transpose [a008578_list, a181363_list]
%o -- _Reinhard Zumkeller_, Mar 22 2014, Oct 20 2011, Oct 16 2010
%K nonn
%O 1,3
%A _Reinhard Zumkeller_, Oct 16 2010
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