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A225318 Numbers n such that either prime(n-1) == -1 (mod n) or prime(n+1) == -1 (mod n) but not both.

%I A225318 #24 Feb 02 2015 05:59:32
%S A225318 2,4,7,8,14,16,26,27,32,33,35,76,78,169,170,172,175,177,183,184,185,
%T A225318 434,446,1054,1056,2638,2702,6468,15930,40069,40070,40080,40112,40115,
%U A225318 40157,251721,251758,251767,251770,251788,637286,4124464,4124704
%N A225318 Numbers n such that either prime(n-1) == -1 (mod n) or prime(n+1) == -1 (mod n) but not both.
%e A225318 2nd prime is 3 and 2 is a member because 1st prime, 2, is congruent to 0 mod 2 and 3rd prime, 5, is congruent to -1 mod 2;
%e A225318 6th prime is 11 and 6 is not a member because 5th prime, 11, is congruent to -1 mod 6 and 7th prime, 17, is congruent to -1 mod 6;
%e A225318 7th prime is 17 and 7 is a member because 6th prime, 13, is congruent to -1 mod 7 and 8th prime, 19, is congruent to 1 mod 6;
%e A225318 14th prime is 43 and 14 is a member because 13th prime, 41, is congruent to -1 mod 14 and 15th prime, 47, is congruent to 5 mod 14.
%p A225318 for n from 2 to 100000 do
%p A225318     if modp(ithprime(n-1),n) = modp(-1,n) then
%p A225318         pn := true ;
%p A225318     else
%p A225318         pn := false ;
%p A225318     end if;
%p A225318     if modp(ithprime(n+1),n) = modp(-1,n) then
%p A225318         pm := true ;
%p A225318     else
%p A225318         pm := false ;
%p A225318     end if;
%p A225318     if pn <> pm then
%p A225318         printf("%d,",n) ;
%p A225318     end if;
%p A225318 end do: # _R. J. Mathar_, May 09 2013
%o A225318 (PARI) is(n)=my(p=prime(n-1),q=nextprime(nextprime(p+1)+1),v=[p+1,q+1]%n); !vecmin(v) && vecmax(v) \\ _Charles R Greathouse IV_, Mar 18 2014
%Y A225318 Cf. A038700, A045924, A078931, A219109.
%K A225318 nonn
%O A225318 1,1
%A A225318 _Irina Gerasimova_, May 05 2013
%E A225318 Corrected by _R. J. Mathar_, May 09 2013
%E A225318 a(36)-a(43) from _Alois P. Heinz_, May 18 2013