OFFSET
0,3
COMMENTS
The prime number theorem implies prime(n) ~ n log n, which explains that lim_{n->oo} A033844(n+1)/A033844(n) = 2. This motivated the present sequence, which has the same property again, e.g., a(46..55)~[1,2,4,8,16,32,64,128,256,512]*10^14. This can be proved by considering an asymptotic expression for prime(n) involving more terms, which yields a(n) = 2^n*(2*log(2)+2/n+O(1/n^2)).
LINKS
M. F. Hasler, Table of n, a(n) for n = 0..55
Wikipedia, Prime number theorem.
PROG
CROSSREFS
KEYWORD
sign
AUTHOR
M. F. Hasler, Oct 09 2011
STATUS
approved