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

1,2

Comments

Occurred when analyzing A056753 to construct a recurrence.

Links

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

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).

Mathematica

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

Prog

(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
(Python)
from oeis_sequences.OEISsequences import bisection, bsearch
def A164632(n):
    if n == 1: return 1
    def g(x): return x+((1<<(x<<1))-1<<1)//3
    def f(x): return n-1+bsearch(g, x)
    return 1<<bisection(f, n-1, n-1)-n+2 # Chai Wah Wu, Mar 01 2026

Crossrefs

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

Sequence in context: A283207 A164717 A164715 * A063095 A156726 A395372

Adjacent sequences: A164629 A164630 A164631 * A164633 A164634 A164635

Keyword

nonn

Author

Reinhard Zumkeller, Aug 23 2009

Extensions

Typo in formula fixed by Reinhard Zumkeller, Oct 16 2010

Status

approved