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

1,1

Links

Table of n, a(n) for n=1..43.

Example

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.

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

Prog

(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

Crossrefs

Cf. A038700, A045924, A078931, A219109.

Sequence in context: A102824 A324588 A201364 * A308267 A177805 A003591

Adjacent sequences: A225315 A225316 A225317 * A225319 A225320 A225321

Keyword

nonn

Author

Irina Gerasimova, May 05 2013

Extensions

Corrected by R. J. Mathar, May 09 2013

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

Status

approved