A166134 a(n+1) is the smallest divisor of a(n)^2+1 that does not yet appear in the sequence, with a(1) = 1.

1, 2, 5, 13, 10, 101, 5101, 26, 677, 45833, 65, 2113, 446477, 130, 16901, 41, 29, 421, 17, 58, 673, 45293, 25, 313, 97, 941, 34057, 50, 61, 1861, 1229, 773, 59753, 89, 34, 1157, 82, 269, 194, 617, 38069, 55740337, 145, 10513, 11052317, 12215371106849

Offset: 1

Author

Franklin T. Adams-Watters, Oct 07 2009

Keywords

• nonn

Comments

All members of the sequence can be represented as the sum of two relatively prime numbers (A008784). It appears that the sequence is infinite and that all such numbers are present.

Examples

			After a(4)=13, the divisors of 13^2+1=170 are 1,2, 5, 10, 17, 34, 85, 170. 1, 2, and 5 have already occurred, so a(5) = 10.
		

Links

• Ivan Neretin, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A166133, A008784, A031439, A002522.

Programs

Mathematica

Nest[Append[#, Min[Complement[Divisors[#[[-1]]^2 + 1], #]]] &, {1}, 45] (* Ivan Neretin, Sep 03 2015 *)

PARI

invec(v,x,n)=for(i=1,n,if(v[i]==x,return(1)));0
bl(n)={local(v,d,ds);
v=vector(n,i,1);
for(i=2,n,
ds=divisors(v[i-1]^2+1);
for(k=2,#ds,d=ds[k];if(!invec(v,d,i-1),v[i]=d;break)));
v}