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

1,3

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.

Links

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

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

Example

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

Prog

(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

Crossrefs

Sequence in context: A321272 A321270 A030067 * A105800 A365859 A105602

Adjacent sequences: A181360 A181361 A181362 * A181364 A181365 A181366

Keyword

nonn

Author

Reinhard Zumkeller, Oct 16 2010

Status

approved