A260623 - OEIS

%I #21 May 08 2021 08:37:05

%S 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,

%T 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,

%U 7,3,0,4,5,6,7,5,6,1,7,5,0,1,6,7,7,8,6

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

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

%H Hiroaki Yamanouchi, <a href="/A260623/b260623.txt">Table of n, a(n) for n = 1..100</a>

%e 1.4257...

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

%o (PARI) solve(x=1.1, 2, zeta(x) - sumeulerrat(1/p, x) - 2) \\ _Michel Marcus_, May 07 2021

%Y For the prime analog, see A243350.

%K nonn,cons

%O 1,2

%A _Matthew Campbell_, Oct 06 2015

%E a(6) corrected and a(7)-a(87) added by _Hiroaki Yamanouchi_, Nov 12 2015