A073718 -id:A073718 - cp's OEIS frontend

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

Asher Auel

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

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

Vincenzo Librandi, Table of n, a(n) for n = 1..200
Index to divisibility sequences.

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

Cf. A184082, A184083.

a034785 = (2 ^) . a000040
-- Reinhard Zumkeller, Feb 07 2015, Jan 24 2012

[2^p: p in PrimesUpTo(100)]; // Vincenzo Librandi, Apr 29 2014

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

a(n)=1<Charles R Greathouse IV, Apr 07 2012

from sympy import prime
def A034785(n): return 1<Chai Wah Wu, Aug 09 2024

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)

More terms from James Sellers, Feb 04 2000

A275306 Decimal expansion of 1/2 - Sum_{k>=1} 1/2^prime(k).

Original entry on oeis.org

0, 8, 5, 3, 1, 7, 4, 9, 0, 1, 4, 8, 8, 8, 8, 3, 3, 9, 7, 5, 1, 8, 9, 0, 3, 7, 7, 8, 4, 5, 6, 9, 2, 2, 9, 1, 6, 3, 4, 2, 2, 5, 7, 6, 1, 8, 6, 2, 0, 8, 3, 0, 2, 2, 1, 3, 1, 7, 5, 4, 5, 8, 5, 5, 1, 1, 3, 5, 9, 0, 3, 9, 3, 8, 0, 6, 4, 2, 6, 6, 5, 8, 0, 3, 7, 0, 9, 9, 5, 1, 5, 7, 1, 5, 2, 4, 2, 2, 2, 0, 6, 0, 3, 8, 3, 8, 4, 0, 6, 4, 7, 9, 1, 7, 0, 1, 4, 0, 4, 2, 1

Offset: 0

Ilya Gutkovskiy, Jul 22 2016

Composite constant: decimal value of A066247 interpreted as a binary number.
The characteristic function of composite numbers (A066247) has values 0, 0, 0, 1, 0, 1, 0, 1, 1, ... for n = 1, 2, 3, ... The constant obtained by concatenating these digits and interpreting them as a binary fraction is therefore C = 0.0001010111010... (base 2) = 0.0853174901...(base 10).
Continued fraction [0; 11, 1, 2, 1, 1, 2, 1, 1, 131, 2, 1, 1, 2, 6, 4, 2, 21, ...].

			0.0853174901... = (0.00010101110...)_2.
                        | | |||
                        4 6 8910

Simon Plouffe, Primes coded in binary to 1000 digits.
Eric Weisstein's World of Mathematics, Composite Number.
Eric Weisstein's World of Mathematics, Prime Constant.

Cf. A002808, A051006, A005171, A062298, A066247, A073718.

nn = 121; Take[#, nn] &@ PadLeft[First@ #, Abs@ Last@ # + Length@ First@ #] &@ RealDigits@ N[1/2 - Sum[ 1/2^Prime[k], {k, 10^4}], nn + 2] (* Michael De Vlieger, Jul 22 2016 *)

s=.5; forprime(p=2,bitprecision(s)+2, s-=1.>>p); s \\ Charles R Greathouse IV, Jul 22 2016

Equals Sum_{k>=1} 1/2^A002808(k).
From Amiram Eldar, Aug 11 2020: (Start)
Equals Sum_{k>=1} 1/A073718(k).
Equals Sum_{k>=1} A066247(k)/2^k.
Equals -(1/2) + Sum_{k>=1} A062298(k)/2^(k+1). (End)
Equals Sum_{k >= 1} ((-1)^A010051(k))/2^(k+1). - Antonio Graciá Llorente, Jan 13 2024

cp's OEIS Frontend

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

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