A034785 a(n) = 2^(n-th prime).

4, 8, 32, 128, 2048, 8192, 131072, 524288, 8388608, 536870912, 2147483648, 137438953472, 2199023255552, 8796093022208, 140737488355328, 9007199254740992, 576460752303423488, 2305843009213693952

Offset

1,1

Comments

These are the "outputs" in Conway's PRIMEGAME (see A007542). - Alonso del Arte, Jan 03 2011

Multiplicative encoding of the n-th prime. - Daniel Forgues, Feb 26 2017

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index to divisibility sequences.

Formula

From Amiram Eldar, Aug 11 2020: (Start)

a(n) = 2^A000040(n).

Sum_{n>=1} 1/a(n) = A051006. (End)

From Amiram Eldar, Nov 22 2022: (Start)

Product_{n>=1} (1 + 1/a(n)) = A184083.

Product_{n>=1} (1 - 1/a(n)) = A184082. (End)

Example

a(4) = 128 because the fourth prime number is 7 and 2^7 = 128.

Mathematica

2^Prime@Range@40  (* Vladimir Joseph Stephan Orlovsky, Apr 11 2011 *)

Prog

(Haskell)
a034785 = (2 ^) . a000040
-- Reinhard Zumkeller, Feb 07 2015, Jan 24 2012
(PARI) a(n)=1<<prime(n) \\ Charles R Greathouse IV, Apr 07 2012
(Magma) [2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi, Apr 29 2014

Crossrefs

Cf. A000040, A000430, A051006, A073718 (2^(n-th composite)), A074736.

Cf. A184082, A184083.

Sequence in context: A327493 A103970 A227295 * A247938 A072868 A075398

Adjacent sequences: A034782 A034783 A034784 * A034786 A034787 A034788

Keyword

easy,nonn

Author

Asher Auel

Extensions

More terms from James A. Sellers, Feb 04 2000

Status

approved