A069485 Greatest prime factor of prime(n+1)^2 + prime(n)^2.

13, 17, 37, 17, 29, 229, 13, 89, 137, 53, 233, 61, 353, 2029, 193, 37, 277, 821, 953, 61, 89, 101, 1481, 1733, 53, 2081, 269, 2333, 29, 14449, 3329, 3593, 293, 1597, 22501, 73, 25609, 373, 28909, 6197, 32401, 389, 101, 2237, 7841, 42061, 29, 257, 281, 821

Offset

1,1

Comments

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

Links

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

Formula

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

Example

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

Maple

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

Mathematica

Table[ FactorInteger[ Prime[n + 1]^2 + Prime[n]^2] [[ -1, 1]], {n, 1, 50} ]
FactorInteger[#][[-1, 1]]&/@Total/@Partition[Prime[Range[60]]^2, 2, 1] (* Harvey P. Dale, Jul 08 2019 *)

Prog

(PARI) gpf(n)=my(f=factor(n)[, 1]); f[#f]
a(n)=my(p=prime(n)); gpf(nextprime(p+1)^2 + p^2) \\ Charles R Greathouse IV, May 14 2014

Crossrefs

Cf. A069483.

Sequence in context: A126808 A053009 A377465 * A263725 A340053 A174056

Adjacent sequences: A069482 A069483 A069484 * A069486 A069487 A069488

Keyword

nonn

Author

Reinhard Zumkeller, Mar 29 2002

Extensions

Edited and extended by Robert G. Wilson v, Apr 18 2002

Status

approved