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

1,1

Comments

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

Links

Table of n, a(n) for n=1..52.

Example

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.

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:

Crossrefs

Cf. A002522, A002144, and A002314.

Sequence in context: A003820 A112980 A109336 * A343905 A232591 A098869

Adjacent sequences: A180339 A180340 A180341 * A180343 A180344 A180345

Keyword

nonn

Author

Michel Lagneau, Jan 18 2011

Status

approved