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A227770
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Bertrand primes II: a(n) is the largest prime < 2*a(n-1)-2.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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).
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MATHEMATICA
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NestList[NextPrime[2 # - 2, -1] &, 5, 40]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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