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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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3
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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, 257, 588, 3423, 3334, 5907, 12882, 1213, 12972, 8547, 3644, 7035, 2178, 16747, 24324, 5523, 12628, 2241, 25602, 16495, 41706, 23127, 22376, 24927
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OFFSET
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2,2
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COMMENTS
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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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LINKS
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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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MATHEMATICA
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fm[n_]:=Module[{n2=n^n, m=1}, While[!PrimeQ[n2+m]||!PrimeQ[n2-m], m++]; m]; Array[fm, 50, 2] Harvey P. Dale, May 19 2012
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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