A193164 a(1) = 1 ; for n > 1, a(n) is the smallest number such that a(n)^2 + 1 contains n distinct prime divisors dividing a(n+1)^2 + 1.

1, 3, 13, 47, 463, 25683, 4187997

Offset: 1

Author

Michel Lagneau, Jul 17 2011

Keywords

• nonn

Comments

This sequence is not the same as A180278.

Examples

			a(1) = 1^1 + 1 = 2 ;
a(2) = 3^2 + 1 = 2*5 ;
a(3) = 13^2 + 1 = 2*5*17 ;
a(4) = 47^2 + 1 = 2*5*13*17 ;
a(5) = 463^2 + 1 = 2*5*13*17*97 ;
a(6) = 25683^2 + 1 = 2 * 5 * 13 * 17 ^ 2 * 97 * 181 ;
a(7) = 4187997^2 + 1 = 2 * 5 * 13 * 17 * 97 * 181 * 452033.
		

Crossrefs

Cf. A180278.

Programs

Maple

with(numtheory):A:={2}:for n from 1 to 7 do:id:=0:for k from 1 to 4200000 (id=0) do:x:=k^2+1:y:=factorset(x):n1:=nops(y):if n1=n and A intersect y = A then A:=y:id:=1:printf ( "%d %d \n",n,k):else fi:od:od: