A382234 Decimal expansion of the multiple prime zeta value primezetamult(2, 2).

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

Offset: 0

Author

Artur Jasinski, Mar 20 2025

Keywords

• cons
• nonn

Comments

Prime multi zeta functions are equivalents of multi zeta functions when successive natural numbers are replaced by successive primes.

Examples

			0.0637672945847765432801316294807
		

Links

• Artur Jasinski, Complete list of multiple prime zeta values up to weight 6.
• Index to constants which are prime multiple zeta values (2,2)

Crossrefs

Cf. A382235, A382236, A197110.

Programs

Mathematica

kk = RealDigits[(PrimeZetaP[2]^2 - PrimeZetaP[4])/2, 10, 105][[1]]; Prepend[kk, 0]

Formula

Equals (A085548^2 - A085964)/2.

Equals Sum_{p,q prime p>q} 1/(p^2*q^2).