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A078611
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Radius of the shortest interval (of positive length) centered at prime(n) that has prime endpoints.
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7
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2, 4, 6, 6, 6, 12, 6, 12, 12, 6, 12, 24, 6, 6, 12, 18, 6, 12, 6, 18, 24, 18, 30, 12, 6, 6, 30, 24, 24, 18, 30, 12, 18, 12, 6, 36, 30, 6, 12, 18, 42, 30, 30, 42, 12, 60, 30, 48, 6, 12, 30, 12, 6, 6, 12, 42, 6, 12, 54, 24, 24, 42, 36, 36, 18, 30, 36, 18, 6, 42, 30, 6, 30, 36, 30, 24, 18, 12
(list; graph; refs; listen; history; internal format)
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OFFSET
| 3,1
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COMMENTS
| a(1) and a(2) are undefined. Alternatively, a(n) = least k, 1 < k < n, such that prime(n) + k and prime(n) - k are both prime. 2. I conjecture that a(n) is defined for all n > 2. Equivalently, every prime > 3 is the average of two distinct primes.
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EXAMPLE
| prime(3) = 5 is the center of the interval [3,7] that has prime endpoints; this interval has radius = 7-5 = 2. Hence a(3) = 2. prime(5) = 11 is the center of the interval [5,17] that has prime endpoints; this interval has radius = 17-11 = 6. Hence a(5) = 6.
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MATHEMATICA
| f[n_] := Module[{p, k}, p = Prime[n]; k = 1; While[(k < p) && (! PrimeQ[p - k] || ! PrimeQ[p + k]), k = k + 1]; k]; Table[f[i], {i, 3, 103}]
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CROSSREFS
| Sequence in context: A174342 A111150 A166983 * A131450 A114218 A111973
Adjacent sequences: A078608 A078609 A078610 * A078612 A078613 A078614
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KEYWORD
| nonn
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AUTHOR
| Joseph L. Pe (joseph_l_pe(AT)hotmail.com), Dec 09 2002
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