A181363 1 followed by the primes, interleaved recursively.

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, 43, 17, 47, 1, 53, 19, 59, 7, 61, 23, 67, 3, 71, 29, 73, 11, 79, 31, 83, 2, 89, 37, 97, 13, 101, 41, 103, 5, 107, 43, 109, 17, 113, 47, 127, 1, 131, 53, 137, 19, 139, 59, 149, 7, 151, 61

Offset: 1

Author

Reinhard Zumkeller, Oct 16 2010

Keywords

• nonn

Comments

a(2*n-1) = A008578(n); a(2*n+1) = A000040(n);

a((2*n-1)*2^k) = A008578(n), k >= 0;

a(2^k) = 1, k >= 0; a(2^k - 1) = A051438(k), k > 0.

Examples

			Initial values, seen as a binary tree:
................................. 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__43...17__47
		

Links

• R. Zumkeller, Table of n, a(n) for n = 1..8191

Programs

Haskell

import Data.List (transpose)
a181363 n = a181363_list !! (n-1)
a181363_list = concat $ transpose [a008578_list, a181363_list]
-- Reinhard Zumkeller, Mar 22 2014, Oct 20 2011, Oct 16 2010

Formula

a(n) = if even n then a(n/2) else A008578((n+1)/2).

a(n) = A008578(A025480(n-1)+1). - Reinhard Zumkeller, Mar 22 2014