A166134 - OEIS

%I #5 Sep 03 2015 18:49:22

%S 1,2,5,13,10,101,5101,26,677,45833,65,2113,446477,130,16901,41,29,421,

%T 17,58,673,45293,25,313,97,941,34057,50,61,1861,1229,773,59753,89,34,

%U 1157,82,269,194,617,38069,55740337,145,10513,11052317,12215371106849

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

%C 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.

%H Ivan Neretin, <a href="/A166134/b166134.txt">Table of n, a(n) for n = 1..1000</a>

%e 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.

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

%o (PARI) invec(v,x,n)=for(i=1,n,if(v[i]==x,return(1)));0

%o bl(n)={local(v,d,ds);

%o v=vector(n,i,1);

%o for(i=2,n,

%o ds=divisors(v[i-1]^2+1);

%o for(k=2,#ds,d=ds[k];if(!invec(v,d,i-1),v[i]=d;break)));

%o v}

%Y Cf. A166133, A008784, A031439, A002522.

%K nonn

%O 1,2

%A _Franklin T. Adams-Watters_, Oct 07 2009