A164632 a(1) = 1 followed by 2^k appearing 2^(2*k-1) times for k>0.

1, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Reinhard Zumkeller, Aug 23 2009

Keywords

• nonn

Comments

Occurred when analyzing A056753 to construct a recurrence.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A004171, A056753, A081294, A053644.

Programs

Haskell

a164632 n = a164632_list !! (n-1)
a164632_list = 1 : concatMap (\x -> replicate (2^(2*x-1)) (2^x)) [1..]
-- Reinhard Zumkeller, Feb 24 2012, Oct 17 2010

Mathematica

Join[{1}, Flatten@Table[2^k, {k, 1, 4}, {2^(2*k - 1)}]] (* Amiram Eldar, Apr 03 2025 *)

Formula

a(n) = f(n,1,1) with f(x,y,z) = if x=1 then z else if y=1 then f(x-1,2*z*z,2*z) else f(x-1,y-1,z).

Extensions

Typo in formula fixed by Reinhard Zumkeller, Oct 16 2010