A138479 a(n) = smallest prime p such that 2n + 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

1,1

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Near-Square Prime

Example

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

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

Crossrefs

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

Sequence in context: A204903 A054906 A269733 * A202106 A136019 A242017

Adjacent sequences: A138476 A138477 A138478 * A138480 A138481 A138482

Keyword

nonn

Author

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

Extensions

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

Status

approved