%I #22 Jul 08 2019 14:50:39

%S 13,17,37,17,29,229,13,89,137,53,233,61,353,2029,193,37,277,821,953,

%T 61,89,101,1481,1733,53,2081,269,2333,29,14449,3329,3593,293,1597,

%U 22501,73,25609,373,28909,6197,32401,389,101,2237,7841,42061,29,257,281,821

%N Greatest prime factor of prime(n+1)^2 + prime(n)^2.

%C How small can members of this sequence be? For example, a(52837) = 97 since 650107^2 + 650099^2 = 2 * 5^4 * 29 * 37 * 73 * 89 * 97. - _Charles R Greathouse IV_, May 14 2014

%H Robert Israel, <a href="/A069485/b069485.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) = A006530(A069484(n)).

%e A069482(10) = A000040(11)^2 + A000040(10)^2 = 29^2 + 31^2 = 841 + 961 = 1802 = 2*17*53, therefore a(10) = 53.

%p seq(max(map2(op,1,ifactors(ithprime(i+1)^2 + ithprime(i)^2)[2])), i=1..1000); # _Robert Israel_, May 18 2014

%t Table[ FactorInteger[ Prime[n + 1]^2 + Prime[n]^2] [[ -1, 1]], {n, 1, 50} ]

%t FactorInteger[#][[-1,1]]&/@Total/@Partition[Prime[Range[60]]^2,2,1] (* _Harvey P. Dale_, Jul 08 2019 *)

%o (PARI) gpf(n)=my(f=factor(n)[,1]); f[#f]

%o a(n)=my(p=prime(n)); gpf(nextprime(p+1)^2 + p^2) \\ _Charles R Greathouse IV_, May 14 2014

%Y Cf. A069483.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Mar 29 2002

%E Edited and extended by _Robert G. Wilson v_, Apr 18 2002