A260623 Decimal expansion of the real solution x to zeta(x) - primezeta(x) = 2.

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

Offset

1,2

Comments

This is also the solution x to Sum_{c composite}(1/c^x) = 1.

Links

Hiroaki Yamanouchi, Table of n, a(n) for n = 1..100

Example

1.4257...

Mathematica

x /. FindRoot[Zeta[x] - PrimeZetaP[x] == 2, {x, 3/2}, WorkingPrecision -> 100] // RealDigits // First (* Jean-François Alcover, May 07 2021 *)

Prog

(PARI) solve(x=1.1, 2, zeta(x) - sumeulerrat(1/p, x) - 2) \\ Michel Marcus, May 07 2021

Crossrefs

For the prime analog, see A243350.

Sequence in context: A241132 A173921 A003572 * A199625 A020849 A134235

Adjacent sequences: A260620 A260621 A260622 * A260624 A260625 A260626

Keyword

nonn,cons

Author

Matthew Campbell, Oct 06 2015

Extensions

a(6) corrected and a(7)-a(87) added by Hiroaki Yamanouchi, Nov 12 2015

Status

approved