A227770 Bertrand primes II: a(n) is the largest prime < 2*a(n-1)-2.

5, 7, 11, 19, 31, 59, 113, 223, 443, 883, 1759, 3511, 7019, 14033, 28057, 56101, 112199, 224363, 448703, 897401, 1794787, 3589571, 7179127, 14358247, 28716487, 57432961, 114865903, 229731787, 459463553, 918927083, 1837854119, 3675708217, 7351416419, 14702832827, 29405665651, 58811331281, 117622662557, 235245325061, 470490650107, 940981300211, 1881962600417

Offset: 1

Author

Jonathan Sondow, Jul 30 2013

Keywords

• nonn

Comments

A strong form of Bertrand's postulate (Chebyshev's theorem) says there exists a prime number p with n < p < 2*n - 2 if n > 3.

The first prime > 3 is 5, so the sequence begins a(1) = 5.

For references, links, and crossrefs, see A006992 (Bertrand primes I).

Examples

			The largest prime < 2*a(1)-2 = 2*5-2 = 8 is 7, so a(2) = 7 = A006992(4).
The largest prime < 2*a(2)-2 = 2*7-2 = 12 is 11, so a(3) = 11 < 13 = A006992(5).
		

Crossrefs

Cf. A006992.

Programs

Mathematica

NestList[NextPrime[2 # - 2, -1] &, 5, 40]