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A120384
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Isolated primes: geometric mean of distances of a prime to neighboring primes sets record.
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1
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3, 5, 7, 23, 53, 89, 113, 211, 1259, 1327, 1847, 2179, 2503, 5623, 14107, 19661, 24281, 38501, 58831, 268343, 396833, 1272749, 2198981, 3863107, 4411963, 4958131, 5102953, 7950001, 8917523, 10938023, 12623189, 22440841, 24662467, 32616223
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OFFSET
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1,1
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COMMENTS
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A096265 is based on arithmetic mean or total distance to neighbors. But it doesn't say if it is isolated from them or close to one of them.
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LINKS
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EXAMPLE
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a(4) = 23 because the distance (geometric mean) to its neighbors (19 and 29) equals = sqrt(4*6) = 4.8989. No smaller prime is more isolated. The next more isolated prime a(5) is 53.
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PROG
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(PARI) lista(nn) = {d = 0; p = 1; q = 2; r = 3; for (i=1, nn, p = q; q = r; r = nextprime(r+1); if ((nd = (q-p)*(r-q)) > d, print1(q, ", "); d = nd; ); ); } \\ Michel Marcus, Jun 12 2013
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Alexis Monnerot-Dumaine (alexis.monnerotdumaine(AT)gmail.com), Jun 29 2006
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EXTENSIONS
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STATUS
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approved
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