OFFSET
5,1
COMMENTS
a(9) has 145 digits and is too large to include.
Conjecture: a(n) < f(n) = number of primes of the form k*2^(n+2) + 1 with k odd that exist between a = 2^(n+2) + 1 and b = floor((2^(2^n) + 1)/(3*2^(n+2) + 1)).
For comparison, f(5) = 5746.
If the extended Riemann hypothesis is true, then for every fixed epsilon > 0, f(n) = Li(b)/(a - 1) + O(b^(1/2 + epsilon)), where Li(b) = integral(2..b, dt/log(t)).
REFERENCES
P. Borwein, S. Choi, B. Rooney and A. Weirathmueller, The Riemann Hypothesis: A Resource for the Aficionado and Virtuoso Alike, Springer, Berlin, 2008, pp. 57-58.
LINKS
Eric Weisstein's World of Mathematics, Fermat Number
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Arkadiusz Wesolowski, Oct 01 2013
STATUS
approved