A098829 - OEIS

%I #10 Feb 19 2018 17:21:46

%S 1,8,2,0,7,1,7,3,3,8,8,1,1,2,7,8,3,7,9,8,6,1,3,3,6,9,7,3,5,0,6,1,5,9,

%T 1,2,8,8,6,7,8,8,8,2,9,5,5,1,4,9,8,9,4,1,3,3,6,7,9,6,4,1,8,3,8,7,3,7,

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

%N Decimal expansion of the infinite sum: each n-th prime number A000040(n) divided by each n-th Fibonacci number A000045(n), from n=1.

%e 18.207173388112783798613369735061591288678882955149894133679641838737...

%p A000040:=n->ithprime(n); A000045:=n->(1/sqrt(5))*(((1+sqrt(5))/2)^n-(2/(1+sqrt(5)))^n*cos(n*Pi)); evalf[82](sum(A000040(k)/A000045(k),k=1..5000)); evalf[82](sum(A000040(k)/A000045(k),k=1..10000));

%t s = 0; Do[s = N[s + Prime[n]/Fibonacci[n], 128], {n, 10^3}]; RealDigits[s, 10, 105][[1]] (* _Robert G. Wilson v_, Nov 04 2004 *)

%t RealDigits[Total[Table[Prime[n]/Fibonacci[n],{n,5000}]],10,120][[1]] (* _Harvey P. Dale_, Feb 19 2018 *)

%o (PARI) suminf(n=1,prime(n)/fibonacci(n)) \\ _Charles R Greathouse IV_, Aug 07 2012

%Y Cf. A000040, A000045.

%K cons,nonn

%O 2,2

%A Joseph Biberstine (jrbibers(AT)indiana.edu), Nov 02 2004

%E More terms from _Robert G. Wilson v_, Nov 04 2004