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Search: id:A075468
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| A075468 |
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Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m. |
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+0
4
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| 1, 4, 15, 42, 7, 186, 75, 10, 33, 1302, 487, 114, 297, 58, 2253, 1980, 1045, 1638, 1767, 2032, 8067, 10800, 427, 588, 9393, 3334, 5907, 50088, 1213, 16662, 8547, 3644, 17853, 2178, 16747, 24324, 5523, 25330, 64467, 42042, 43417, 41706
(list; graph; listen)
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OFFSET
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2,2
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COMMENT
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n^n is an interprime, the average of two consecutive primes, presumably only for n = 2, 6 and 9. In general n^n may be average of several pairs of primes, in which case the minimal distance is in the sequence. It is not clear (but quite probable) that for all n, n^n is the average of two primes. See also n! and n!! as average of two primes in A075409 and A075410.
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FORMULA
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n^n -/+ a(n) are both primes, with a(n) being the smallest common distance.
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EXAMPLE
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a(4)=15 because 4^4=256 and 256 -/+ 15 = 271 and 241 are primes with smallest distance from 4^4; a(23)= 10800 because 23^23 = 20880467999847912034355032910567 and 23^23 -/+ 10800 are two primes with the smallest distance from 23^23.
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CROSSREFS
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Cf. A075469, A075409, A075410.
Sequence in context: A074033 A093920 A011844 this_sequence A100503 A085829 A085567
Adjacent sequences: A075465 A075466 A075467 this_sequence A075469 A075470 A075471
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KEYWORD
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nonn
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AUTHOR
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Zak Seidov (zakseidov(AT)yahoo.com), Sep 18 2002
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EXTENSIONS
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More terms from Lior Manor (lior.manor(AT)gmail.com) Sep 18 2002
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