A063510 a(1) = 1, a(n) = a(floor(square root(n))) + 1 for n > 1.

1, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4

Offset

1,2

Comments

a(n) = A010096(n) until n = 255, but 5 = a(256) <> A010096(256) = 4.

The least k such that a(k)=n for n >= 2 is given by k = 2^(2^(n-2)) so the closed form for a(n) follows. - Benoit Cloitre, Apr 28 2005

Links

Table of n, a(n) for n=1..105.

Formula

a(1)=1; for n >= 2, a(n) = floor(log(4*log(n)/log(2))/log(2)). - Benoit Cloitre, Apr 28 2005

Equivalently, a(n) = 2 + floor(log_2(log_2(n))) for n > 1. - Charles R Greathouse IV, Dec 19 2011

Prog

(PARI) a(n)=if(n<2, 1, floor(log(4*log(n)/log(2))/log(2)))
(Haskell)
a063510 1 = 1
a063510 n = a063510 (a000196 n) + 1
-- Reinhard Zumkeller, Mar 16 2012

Crossrefs

Cf. A010096.

Cf. A000196.

Sequence in context: A157639 A010096 A230864 * A156878 A214454 A140474

Adjacent sequences: A063507 A063508 A063509 * A063511 A063512 A063513

Keyword

easy,nonn

Author

Reinhard Zumkeller, Jul 30 2001

Status

approved