A069483 Largest prime factor of prime(n+1)^2 - prime(n)^2.

5, 2, 3, 3, 3, 5, 3, 7, 13, 5, 17, 13, 7, 5, 5, 7, 5, 3, 23, 3, 19, 3, 43, 31, 11, 17, 7, 3, 37, 7, 43, 67, 23, 5, 5, 11, 5, 11, 17, 11, 5, 31, 3, 13, 11, 41, 31, 5, 19, 11, 59, 5, 41, 127, 13, 19, 5, 137, 31, 47, 5, 7, 103, 13, 7, 7, 167, 19, 29, 13, 89, 11, 37, 47, 127, 193, 131, 19

Offset: 1

Author

Reinhard Zumkeller, Mar 29 2002, Aug 05 2007

Keywords

• nonn

Examples

			A069482(12) = A000040(13)^2 - A000040(12)^2 = 41^2 - 37^2 = 1681 - 1369 = 312 = 2*2*2*3*13, therefore a(12) = 13.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A006530, A069482, A069485.

Programs

Mathematica

FactorInteger[#[[2]]-#[[1]]][[-1,1]]&/@Partition[Prime[Range[80]]^2,2,1] (* Harvey P. Dale, Jan 17 2016 *)

PARI

a(n) = my(f=factor(prime(n+1)^2 - prime(n)^2)); f[#f~,1]; \\ Michel Marcus, Nov 12 2023

Formula

a(n) = A006530(A069482(n)).