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

1,2

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.

Links

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

Example

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.

Mathematica

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

Prog

(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}

Crossrefs

Cf. A166133, A008784, A031439, A002522.

Sequence in context: A241758 A173620 A319920 * A336883 A067365 A189993

Adjacent sequences: A166131 A166132 A166133 * A166135 A166136 A166137

Keyword

nonn

Author

Franklin T. Adams-Watters, Oct 07 2009

Status

approved