cp's OEIS Frontend

A075468 Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.

%I A075468 #29 Apr 16 2025 05:42:21
%S A075468 1,4,15,42,7,186,75,10,33,1302,487,114,297,58,2253,1980,1045,1638,
%T A075468 1767,2032,8067,10800,257,588,3423,3334,5907,12882,1213,12972,8547,
%U A075468 3644,7035,2178,16747,24324,5523,12628,2241,25602,16495,41706,23127,22376,24927
%N A075468 Minimal m such that n^n-m and n^n+m are both primes, or -1 if there is no such m.
%C A075468 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.
%C A075468 n^n -/+ a(n) are both primes, with a(n) being the smallest common distance.
%H A075468 Sean A. Irvine, <a href="/A075468/b075468.txt">Table of n, a(n) for n = 2..150</a>
%F A075468 a(n) = A082467(A000312(n)). - _Michel Marcus_, Feb 21 2025
%e A075468 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 A075468 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 *)
%o A075468 (PARI) a(n) = my(m=1,nn=n^n); while (! (ispseudoprime(nn-m) && ispseudoprime(nn+m)), m++); m; \\ _Michel Marcus_, Feb 21 2025
%Y A075468 Cf. A075469, A075409, A075410.
%Y A075468 Cf. A000312, A082467.
%K A075468 nonn
%O A075468 2,2
%A A075468 _Zak Seidov_, Sep 18 2002
%E A075468 More terms from _Lior Manor_, Sep 18 2002
%E A075468 Corrected by _Harvey P. Dale_, May 19 2012