cp's OEIS Frontend

A210487 a(n) is the smallest possible greatest prime factor of prime(n)^2 - prime(k)^2 for 0 < k < n.

%I A210487 #19 Apr 17 2013 04:03:01
%S A210487 5,2,3,3,3,5,3,5,5,3,5,3,3,5,5,3,5,3,7,3,5,3,3,5,5,5,5,3,5,5,5,5,5,5,
%T A210487 5,7,5,5,5,5,5,7,3,5,5,7,7,5,7,5,7,5,7,5,5,5,5,5,11,3,5,3,11,5,5,5,7,
%U A210487 5,7,5,7,7,7,7,5,5,7,5,5,7,5,7,3,5,5,5
%N A210487 a(n) is the smallest possible greatest prime factor of prime(n)^2 - prime(k)^2 for 0 < k < n.
%C A210487 a(1) is not defined because there is no prime number smaller than 2.
%H A210487 Lei Zhou, <a href="/A210487/b210487.txt">Table of n, a(n) for n = 2..10000</a>
%e A210487 n = 2, prime(2) = 3, 3^2 - prime(1)^2 = 5; so a(2) = 5;
%e A210487 n = 3, prime(3) = 5, 5^2 - prime(1)^2 = 21 = 3*7; 5^2 - prime(2)^2 = 16 = 2^4; Min(7, 2) = 2, so a(3) = 2.
%p A210487 A210487 := proc(n)
%p A210487     local p,k,pk,a ;
%p A210487     a := ithprime(n)+ithprime(n-1) ;
%p A210487     p := ithprime(n) ;
%p A210487     for k from 1 to n-1 do
%p A210487         kp := ithprime(k) ;
%p A210487         max(A006530(p+kp), A006530(p-kp)) ;
%p A210487         a := min(a,%) ;
%p A210487     end do:
%p A210487     return a ;
%p A210487 end proc: # _R. J. Mathar_, Apr 17 2013
%t A210487 Table[Min[Table[Last[FactorInteger[Prime[i]^2 - Prime[j]^2]][[1]], {j, 1, i - 1}]], {i, 2, 87}]
%Y A210487 Cf. A000040.
%K A210487 nonn,easy
%O A210487 2,1
%A A210487 _Lei Zhou_, Jan 23 2013