A382236 Decimal expansion of the multiple prime zeta value primezetamult(2, 2, 2).

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

Offset: 1

Author

Artur Jasinski, Apr 01 2025

Keywords

• nonn
• cons

Comments

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

For complete list of multiple prime zeta values up to weight 6 see A382234.

Examples

			0.003696244163452835378395534632394668...
		

Crossrefs

Cf. A382234, A382235, A381653.

Programs

Mathematica

kk = {0, 0}; AppendTo[kk, RealDigits[(PrimeZetaP[2]^3 - 3 PrimeZetaP[2] PrimeZetaP[4] + 2 PrimeZetaP[6])/6, 10, 105][[1]]]; Flatten[kk]

Formula

Equals (P(2)^3-3*P(2)*P(4)+2*P(6))/6 where P(n) is Prime zeta function.