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A344582
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a(n) is the least k such that there are exactly n primes between prime(k) + 1 and floor(prime(k + 1)^2/prime(k)) (inclusive) or 0 if no such k exists.
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1
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1, 2, 4, 30, 180, 462, 890, 1532, 3385, 19871, 29040, 59257, 66762, 31545, 597311, 1448751, 1421021, 1293698, 12768473, 2279181, 147165284, 118374763, 821495413, 2618883054, 2247521689, 3145845927, 7650216016, 27357920380, 22859974504, 189924891289, 78076882908, 189573830057
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OFFSET
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1,2
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COMMENTS
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a(n) is the least k such that A228098(k) = n.
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LINKS
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Table of n, a(n) for n=1..32.
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EXAMPLE
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a(4) = 30 as there are exactly 4 primes between prime(30) + 1 = 114 and floor(prime(31)^2/prime(30)) = 142 namely the four primes 127, 131, 137 and 139.
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PROG
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(PARI) upto(n) = {my(i, p, q, res = vector(1)); i = 1; p = 2; forprime(q = 3, oo, u = q^2\p; t = 1; forprime(r = q + 1, u, t++); if(t > #res, res = concat(res, vector(t - #res))); if(res[t] == 0, res[t] = i; ); p = q; i++; if(i > n, return(res))); }
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CROSSREFS
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Cf. A228098, A230777.
Sequence in context: A084914 A058779 A230777 * A241542 A241540 A349265
Adjacent sequences: A344579 A344580 A344581 * A344583 A344584 A344585
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KEYWORD
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nonn
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AUTHOR
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David A. Corneth, May 24 2021
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EXTENSIONS
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a(24)-a(32) from Martin Ehrenstein, Jun 02 2021
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STATUS
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approved
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