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

2, 4, 7, 8, 14, 16, 26, 27, 32, 33, 35, 76, 78, 169, 170, 172, 175, 177, 183, 184, 185, 434, 446, 1054, 1056, 2638, 2702, 6468, 15930, 40069, 40070, 40080, 40112, 40115, 40157, 251721, 251758, 251767, 251770, 251788, 637286, 4124464, 4124704

Offset: 1

Author

Irina Gerasimova, May 05 2013

Keywords

• nonn

Examples

			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;
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;
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;
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.
		

Crossrefs

Cf. A038700, A045924, A078931, A219109.

Programs

Maple

for n from 2 to 100000 do
    if modp(ithprime(n-1),n) = modp(-1,n) then
        pn := true ;
    else
        pn := false ;
    end if;
    if modp(ithprime(n+1),n) = modp(-1,n) then
        pm := true ;
    else
        pm := false ;
    end if;
    if pn <> pm then
        printf("%d,",n) ;
    end if;
end do: # R. J. Mathar, May 09 2013

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

Extensions

Corrected by R. J. Mathar, May 09 2013

a(36)-a(43) from Alois P. Heinz, May 18 2013