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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

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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