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

%I A034785 #62 Jul 02 2025 16:01:56
%S A034785 4,8,32,128,2048,8192,131072,524288,8388608,536870912,2147483648,
%T A034785 137438953472,2199023255552,8796093022208,140737488355328,
%U A034785 9007199254740992,576460752303423488,2305843009213693952
%N A034785 a(n) = 2^(n-th prime).
%C A034785 These are the "outputs" in Conway's PRIMEGAME (see A007542). - _Alonso del Arte_, Jan 03 2011
%C A034785 Multiplicative encoding of the n-th prime. - _Daniel Forgues_, Feb 26 2017
%H A034785 Vincenzo Librandi, <a href="/A034785/b034785.txt">Table of n, a(n) for n = 1..200</a>
%H A034785 <a href="/index/Di#divseq">Index to divisibility sequences</a>.
%F A034785 From _Amiram Eldar_, Aug 11 2020: (Start)
%F A034785 a(n) = 2^A000040(n).
%F A034785 Sum_{n>=1} 1/a(n) = A051006. (End)
%F A034785 From _Amiram Eldar_, Nov 22 2022: (Start)
%F A034785 Product_{n>=1} (1 + 1/a(n)) = A184083.
%F A034785 Product_{n>=1} (1 - 1/a(n)) = A184082. (End)
%e A034785 a(4) = 128 because the fourth prime number is 7 and 2^7 = 128.
%t A034785 2^Prime@Range@40  (* _Vladimir Joseph Stephan Orlovsky_, Apr 11 2011 *)
%o A034785 (Haskell)
%o A034785 a034785 = (2 ^) . a000040
%o A034785 -- _Reinhard Zumkeller_, Feb 07 2015, Jan 24 2012
%o A034785 (PARI) a(n)=1<<prime(n) \\ _Charles R Greathouse IV_, Apr 07 2012
%o A034785 (Magma) [2^p: p in PrimesUpTo(100)]; // _Vincenzo Librandi_, Apr 29 2014
%o A034785 (Python)
%o A034785 from sympy import prime
%o A034785 def A034785(n): return 1<<prime(n) # _Chai Wah Wu_, Aug 09 2024
%Y A034785 Cf. A000040, A000430, A051006, A073718 (2^(n-th composite)), A074736.
%Y A034785 Cf. A184082, A184083.
%K A034785 easy,nonn
%O A034785 1,1
%A A034785 _Asher Auel_
%E A034785 More terms from _James Sellers_, Feb 04 2000