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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.

%I A249132 #30 Nov 16 2014 12:02:22
%S A249132 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,
%T A249132 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,
%U A249132 659,0,241,0,2503,0,337,53,0,3671,0,0
%N A249132 Smallest noncomposite k such that prime(n) is the largest prime factor of k^2+1, or 0 if no such k exists.
%C A249132 a(A080148(m)) = 0. - _Joerg Arndt_, Oct 22 2014
%H A249132 Robert Israel, <a href="/A249132/b249132.txt">Table of n, a(n) for n = 1..10000</a>
%e A249132 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).
%p A249132 A249132:= proc(n) local p,i,k,a,b;
%p A249132    p:= ithprime(n);
%p A249132    if p mod 4 = 3 then return 0 fi;
%p A249132    a:= numtheory:-msqrt(-1,p);
%p A249132    if a < p/2 then b:= p-a
%p A249132    else b:= a; a:= p-a
%p A249132    fi;
%p A249132    for i from 0 do
%p A249132     for k in [a+i*p,b+i*p] do
%p A249132       if isprime(k) and p = max(numtheory:-factorset(k^2+1)) then
%p A249132         return(k)
%p A249132       fi
%p A249132     od
%p A249132    od
%p A249132 end proc:
%p A249132 1,seq(A249132(n),n=2..100); # _Robert Israel_, Nov 10 2014
%t A249132 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 *)
%Y A249132 Cf. A080148, A185389, A223702, A223705.
%K A249132 nonn
%O A249132 1,3
%A A249132 _Juri-Stepan Gerasimov_, Oct 22 2014