A249132 Smallest noncomposite k such that prime(n) is the largest prime factor of k^2+1, or 0 if no such k exists.

1, 0, 2, 0, 0, 5, 13, 0, 0, 17, 0, 31, 73, 0, 0, 23, 0, 11, 0, 0, 173, 0, 0, 233, 463, 293, 0, 0, 251, 919, 0, 0, 37, 0, 193, 0, 443, 0, 0, 599, 0, 19, 0, 467, 211, 0, 0, 0, 0, 107, 89, 0, 659, 0, 241, 0, 2503, 0, 337, 53, 0, 3671, 0, 0

Offset: 1

Author

Juri-Stepan Gerasimov, Oct 22 2014

Keywords

• nonn

Comments

a(A080148(m)) = 0. - Joerg Arndt, Oct 22 2014

Examples

			a(1)=1 is in this sequence because 1 is in A008578 and the largest prime factor of 1^2+1 = 2 is prime(1).
		

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A080148, A185389, A223702, A223705.

Programs

Maple

A249132:= proc(n) local p,i,k,a,b;
   p:= ithprime(n);
   if p mod 4 = 3 then return 0 fi;
   a:= numtheory:-msqrt(-1,p);
   if a < p/2 then b:= p-a
   else b:= a; a:= p-a
   fi;
   for i from 0 do
    for k in [a+i*p,b+i*p] do
      if isprime(k) and p = max(numtheory:-factorset(k^2+1)) then
        return(k)
      fi
    od
   od
end proc:
1,seq(A249132(n),n=2..100); # Robert Israel, Nov 10 2014

Mathematica

a249132[n_Integer] := Module[{t = Table[0, {n}], k, s, p}, Do[If[Mod[Prime[k], 4] == 3, t[[k]] = -1], {k, n}]; k = 0; While[Times @@ t == 0, k++; s = FactorInteger[k^2 + 1][[-1, 1]]; p = PrimePi[s]; If[p <= n && t[[p]] == 0 && ! CompositeQ[k], t[[p]] = k]]; t /. -1 -> 0]; a249132[120] (* Michael De Vlieger, Nov 11 2014, adapted from A223702 *)