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A233822
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a(n) = 2*R(n) - R(n+1), where R(n) is the n-th Ramanujan prime.
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4
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-7, 5, 5, 17, 35, 35, 51, 63, 45, 93, 95, 87, 105, 147, 135, 155, 177, 135, 225, 225, 227, 237, 219, 257, 257, 255, 303, 275, 345, 331, 361, 345, 393, 399, 407, 429, 427, 417, 435, 483, 479, 437, 567, 555, 581, 587, 597, 595, 573, 639, 639, 641, 647
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OFFSET
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1,1
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COMMENTS
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Paksoy proved that a(n) > 0 for n > 1.
Paksoy's theorem is the analog for Ramanujan primes of Chebychev's theorem (Bertrand's postulate) that 2*prime(n) - prime(n+1) > 0 for n > 0 (see A062234).
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LINKS
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EXAMPLE
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The only negative term is a(1) = 2*R(1) - R(2) = 2*2 - 11 = -7.
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MATHEMATICA
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nn = 100;
R = Table[0, {nn}]; s = 0; Do[If[PrimeQ[k], s++]; If[PrimeQ[k/2], s--]; If[s < nn, R[[s + 1]] = k], {k, Prime[3*nn]}]; R = R + 1;
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PROG
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(Perl) use ntheory ":all"; say 2*nth_ramanujan_prime($_)-nth_ramanujan_prime($_+1) for 1..10 # Dana Jacobsen, Sep 02 2017
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CROSSREFS
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KEYWORD
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sign
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AUTHOR
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STATUS
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approved
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