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A275306 Decimal expansion of 1/2 - Sum_{k>=1} 1/2^prime(k). 0
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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, ...].

LINKS

Table of n, a(n) for n=0..120.

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

FORMULA

Equals Sum_{k>=1} 1/2^A002808(k).

EXAMPLE

0.0853174901... = (0.00010101110...)_2.

                        | | |||

                        4 6 8910

MATHEMATICA

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 *)

PROG

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

CROSSREFS

Cf. A002808, A051006, A005171, A066247.

Sequence in context: A198918 A196515 A116397 * A176705 A140133 A086723

Adjacent sequences:  A275303 A275304 A275305 * A275307 A275308 A275309

KEYWORD

nonn,cons

AUTHOR

Ilya Gutkovskiy, Jul 22 2016

STATUS

approved

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Last modified May 19 10:36 EDT 2019. Contains 323390 sequences. (Running on oeis4.)