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

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, 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, 5, 7, 5, 7, 7, 7, 7, 5, 5, 7, 5, 5, 7, 5, 7, 3, 5, 5, 5

Offset: 2

Author

Lei Zhou, Jan 23 2013

Keywords

• nonn
• easy

Comments

a(1) is not defined because there is no prime number smaller than 2.

Examples

			n = 2, prime(2) = 3, 3^2 - prime(1)^2 = 5; so a(2) = 5;
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.
		

Links

• Lei Zhou, Table of n, a(n) for n = 2..10000

Crossrefs

Cf. A000040.

Programs

Maple

A210487 := proc(n)
    local p,k,pk,a ;
    a := ithprime(n)+ithprime(n-1) ;
    p := ithprime(n) ;
    for k from 1 to n-1 do
        kp := ithprime(k) ;
        max(A006530(p+kp), A006530(p-kp)) ;
        a := min(a,%) ;
    end do:
    return a ;
end proc: # R. J. Mathar, Apr 17 2013

Mathematica

Table[Min[Table[Last[FactorInteger[Prime[i]^2 - Prime[j]^2]][[1]], {j, 1, i - 1}]], {i, 2, 87}]