A229857 Round(2^(m-n-2)/(m*log(8))), where m = 2^n - n - 2.

5043, 2417158053779, 5245728941618725066052704993134, 215872416866954281715178071724040762825421437510476267629647193878371

Offset: 5

Author

Arkadiusz Wesolowski, Oct 01 2013

Keywords

• nonn
• easy

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

Cf. A000215, A016631, A023394, A046052.