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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
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
1,3
COMMENTS
a(A080148(m)) = 0. - Joerg Arndt, Oct 22 2014
LINKS
EXAMPLE
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).
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 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved