A293258 Decimal expansion of product of 1 - 4^-p over all primes p.

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

Offset

0,1

Comments

Knopfmacher proves that prime(n+1) = floor(1 - log(1 - A/P)) where A is this constant and P is the product (1 - 4^-2)(1 - 4^-3)(1 - 4^-5)...(1 - 4^-prime(n)).

Links

Table of n, a(n) for n=0..104.

John Knopfmacher, Recursive formulae for prime numbers, Archiv der Mathematik (Basel) 33:2 (1979/80), pp. 144-149.

Formula

Equals A184082 * A184083 = A184082 / A184084. - Amiram Eldar, Nov 16 2021

Example

0.921893835296931859194670302799807186732205478738862674976230660393864453122...

Prog

(PARI) prodeuler(p=2, bitprecision(1.)/2+2, 1-4.^-p)

Crossrefs

Cf. A184082, A184083, A184084.

Sequence in context: A154993 A197488 A197757 * A010536 A239908 A293171

Adjacent sequences: A293255 A293256 A293257 * A293259 A293260 A293261

Keyword

nonn,cons

Author

Charles R Greathouse IV, Oct 04 2017

Status

approved