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%I #15 Dec 10 2024 05:39:00
%S 1,4,15,42,7,186,75,10,33,1302,487,114,297,58,2253,1980,1045,1638,
%T 1767,2032,8067,10800,257,588,3423,3334,5907,12882,1213,12972,8547,
%U 3644,7035,2178,16747,24324,5523,12628,2241,25602,16495,41706,23127,22376,24927
%N Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.
%C 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.
%F n^n -/+ a(n) are both primes, with a(n) being the smallest common distance.
%e 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.
%t 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 *)
%Y Cf. A075469, A075409, A075410.
%K nonn,changed
%O 2,2
%A _Zak Seidov_, Sep 18 2002
%E More terms from _Lior Manor_ Sep 18 2002
%E Corrected by _Harvey P. Dale_, May 19 2012