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A075468
Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.
3
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
OFFSET
2,2
COMMENTS
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.
FORMULA
n^n -/+ a(n) are both primes, with a(n) being the smallest common distance.
EXAMPLE
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.
MATHEMATICA
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
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 18 2002
EXTENSIONS
More terms from Lior Manor Sep 18 2002
Corrected by Harvey P. Dale, May 19 2012
STATUS
approved