A129784 a(n) = floor(log_10(2^(2^n))).

0, 1, 2, 4, 9, 19, 38, 77, 154, 308, 616, 1233, 2466, 4932, 9864, 19728, 39456, 78913, 157826, 315652, 631305, 1262611, 2525222, 5050445, 10100890, 20201781, 40403562, 80807124, 161614248, 323228496, 646456993, 1292913986, 2585827972

Offset

1,3

Comments

Starting with 2, n successive squarings yields an (a(n)+1)-digit number.

Dubickas proves that infinitely many terms of this sequence are divisible by 2 or 3 (and hence infinitely many composites). - Charles R Greathouse IV, Feb 04 2016

Links

Table of n, a(n) for n=1..33.

Artūras Dubickas, Prime and composite integers close to powers of a number, Monatsh. Math. 158:3 (2009), pp. 271-284.

Example

a(16) = 19728 because floor(log_10(2^(2^16))) = floor(log_10(2^65536)) = floor(log_10(2.003529930406846*10^19728)) = floor(19728.30179583467) = 19728.

Mathematica

Table[Floor[Log[10, 2^(2^n)]], {n, 1, 29}] (* Vincenzo Librandi, Dec 30 2015 *)

Prog

(Magma) [Floor(Log(10, 2^(2^n))): n in [1..29]]; // Vincenzo Librandi, Dec 30 2015
(PARI) a(n) = floor(log(2^(2^n))/log(10)); \\ Michel Marcus, Dec 30 2015
(PARI) a(n)=logint(2^2^n, 10) \\ impractical except for small n, but avoids rounding; Charles R Greathouse IV, Feb 04 2016

Crossrefs

Cf. A001146.

Sequence in context: A292478 A309267 A262864 * A329356 A125050 A056186

Adjacent sequences: A129781 A129782 A129783 * A129785 A129786 A129787

Keyword

nonn

Author

Jon E. Schoenfield, May 18 2007

Status

approved