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A034785 a(n) = 2^(n-th prime). 37
4, 8, 32, 128, 2048, 8192, 131072, 524288, 8388608, 536870912, 2147483648, 137438953472, 2199023255552, 8796093022208, 140737488355328, 9007199254740992, 576460752303423488, 2305843009213693952 (list; graph; refs; listen; history; text; internal format)
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
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.
Sequence in context: A327493 A103970 A227295 * A247938 A072868 A075398
KEYWORD
easy,nonn
AUTHOR
EXTENSIONS
More terms from James A. Sellers, Feb 04 2000
STATUS
approved

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Last modified May 19 14:45 EDT 2024. Contains 372698 sequences. (Running on oeis4.)