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Numbers n such that either prime(n-1) == -1 (mod n) or prime(n+1) == -1 (mod n) but not both.
0

%I #24 Feb 02 2015 05:59:32

%S 2,4,7,8,14,16,26,27,32,33,35,76,78,169,170,172,175,177,183,184,185,

%T 434,446,1054,1056,2638,2702,6468,15930,40069,40070,40080,40112,40115,

%U 40157,251721,251758,251767,251770,251788,637286,4124464,4124704

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

%e 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 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 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 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 for n from 2 to 100000 do

%p if modp(ithprime(n-1),n) = modp(-1,n) then

%p pn := true ;

%p else

%p pn := false ;

%p end if;

%p if modp(ithprime(n+1),n) = modp(-1,n) then

%p pm := true ;

%p else

%p pm := false ;

%p end if;

%p if pn <> pm then

%p printf("%d,",n) ;

%p end if;

%p end do: # _R. J. Mathar_, May 09 2013

%o (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 Cf. A038700, A045924, A078931, A219109.

%K nonn

%O 1,1

%A _Irina Gerasimova_, May 05 2013

%E Corrected by _R. J. Mathar_, May 09 2013

%E a(36)-a(43) from _Alois P. Heinz_, May 18 2013