A180342 a(n) = the smallest number k such that the smallest prime factor of k^2 + 1 equals A002144(n).

2, 34, 4, 46, 6, 50, 76, 194, 100, 144, 366, 10, 730, 324, 374, 254, 286, 266, 886, 274, 14, 794, 610, 546, 16, 456, 494, 334, 724, 964, 520, 526, 834, 664, 1596, 504, 3510, 20, 2720, 1234, 1120, 516, 566, 874, 810, 756, 1134, 2110, 1224, 24, 670, 726

Offset: 1

Author

Michel Lagneau, Jan 18 2011

Keywords

• nonn

Comments

The sequence giving the smallest number k such that the greatest prime factor of k^2 + 1 equals A002144(n) is A002314.

Examples

			a(1) = 2 because 2^2 + 1 = 5 = A002144(1) ;
a(2) = 34 because 34^2 + 1= 13*89 = A002144(2) * 89 ;
a(3) = 4 because 4^2 + 1 = 17 = A002144(3) ;
a(4) = 46 because 46^2 + 1 = 29*73 = A002144(4) * 73.
		

Crossrefs

Cf. A002522, A002144, and A002314.

Programs

Maple

with(numtheory):T:=array(1..200):k:=1:for p from 1 to 1000 do: if type(p,prime)=true
  and irem(p,4)=1 then T[k]:=p:k:=k+1:else fi:od:for q from 1 to k do:z:=T[q]:ind:=0:for n from 1 to 10000 while(ind=0) do: x:=n^2+1:y:=factorset(x):if z=y[1] then ind:=1:printf(`%d, `,n):else fi:od: od: