A166134 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

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);