A138479 a(n) = smallest prime p such that 2*n + p^2 is another prime, or 0 if no such prime exists.

3, 3, 5, 3, 3, 5, 3, 5, 5, 3, 3, 7, 0, 3, 7, 3, 3, 5, 3, 7, 5, 3, 5, 5, 3, 3, 5, 0, 3, 7, 3, 3, 29, 0, 3, 5, 3, 5, 5, 3, 5, 5, 0, 3, 7, 3, 3, 19, 3, 3, 5, 3, 5, 7, 0, 5, 5, 0, 3, 11, 3, 5, 5, 3, 3, 5, 0, 11, 5, 3, 3, 7, 0, 3, 7, 0, 3, 5, 3, 11, 7, 3, 5, 5, 3, 3, 5, 0, 7, 7, 3, 3, 5, 3, 3, 7, 0, 11, 5, 0

Offset: 1

Author

Philippe LALLOUET (philip.lallouet(AT)orange.fr), Mar 20 2008

Keywords

• nonn

Comments

For numbers k such that a(k) = 0 see A138685.

Examples

			11=2+3^2 hence a(1)=3,
13=4+3^2 hence a(2)=3,
31=6+5^2 hence a(3)=5.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Near-Square Prime

Crossrefs

Cf. A002373, A020481, A049613, A059324 (?).

Programs

Maple

a:= proc(n) local p;
      if irem(n, 3)=1 and not isprime(2*n+9) then 0
    else p:=2;
         do p:= nextprime(p);
            if isprime(2*n+p^2) then return p fi
         od
      fi
    end:
seq(a(n), n=1..100);  # Alois P. Heinz, Jun 16 2014

Mathematica

a = {}; Do[ p = 0; While[ (! PrimeQ[ 2*n + Prime[ p + 1 ]2 ]) && (p < 1000), p++ ]; If[ p < 1000, AppendTo[ a, Prime[ p + 1 ] ], AppendTo[ a, 0 ] ], {n, 1, 150} ]; a (* Artur Jasinski, Mar 26 2008 *)
a[n_]:=If[Mod[n,3]!=1,(For[m=1,!PrimeQ[2n+Prime[m]^2],m++ ]; Prime[m]),If[ !PrimeQ[2n+9],0,3]];Table[a[n],{n,100}] (* Farideh Firoozbakht, Mar 28 2008 *)

Extensions

More terms from Artur Jasinski and Farideh Firoozbakht, Mar 26 2008