1,3

As n increases sum k(n) for i=1 to n / sum n for i=1 to n tends to 1/4 all values in b152414 verified and primes certified using PFGW from Primeform group

Contribution from Pierre CAMI (pierre-cami(AT)orange.fr), Dec 04 2008: (Start)

for n even sum k(2*n) for i=1 to n / sum 2*n for i=1 to n tends to log(2)/4

for n odd sum k(2*n+1) for i=0 to n / sum 2*n+1 for i=1 to n tends to 1/2-log(2)/4

(End)

Pierre CAMI, Table of n, a(n) for n=1..4000

1*2^1*(2^1-1)+1=3 prime so k(1)=1 1*2^2*(2^2-1)-1=11 prime as 13 so k(2)=1 2*2^3*(2^3-1)+1=113 prime so k(3)=2

Sequence in context: A101417 A035636 A104554 this_sequence A120013 A151847 A113749

Adjacent sequences: A152411 A152412 A152413 this_sequence A152415 A152416 A152417

nonn

Pierre CAMI (pierre-cami(AT)orange.fr), Dec 03 2008