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A181363 1 followed by the primes, interleaved recursively.

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