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