A034785 - OEIS

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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 (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	`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`

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Last modified June 2 15:24 EDT 2024. Contains 373040 sequences. (Running on oeis4.)