cp's OEIS Frontend

A282538 Odd integers n with the property that the largest prime factor of n^2+4 is less than n.

%I A282538 #12 Feb 18 2017 22:32:26
%S A282538 11,29,49,59,99,111,121,127,141,161,179,199,205,211,213,219,237,247,
%T A282538 261,283,289,309,311,335,359,369,387,393,411,417,419,433,441,469,479,
%U A282538 485,521,523,527,535,569,581,595,603,611,619,621,633,643,679,691,705,711,715,723,729,739,741,749,759
%N A282538 Odd integers n with the property that the largest prime factor of n^2+4 is less than n.
%C A282538 Every Pythagorean prime p can be uniquely written as the sum of two positive integers a and b such that ab is congruent to 1 (mod p).  If a>b, then the difference a-b must be an odd number; no number on this list can be said difference, and every positive odd integer NOT on this list is the difference of exactly one pair.
%e A282538 Examples: 5 is not on this list, and 17-12=5 while 17+12=29 and (17)(12)==1 mod 29.  9 is not on this list, and 13-4=9 while 13+4=17 and (13)(4)==1 mod 17.  13 is not on this list, and 93-80=13 while 93+80=173 and (93)(80)==1 mod 173.  Note that 5^2+4=29, 9^2+4=85=17(5), and 13^2+4=173
%t A282538 fQ[n_] := FactorInteger[n^2 + 4][[-1, 1]] < n; Select[2 Range[380] - 1, fQ] (* _Robert G. Wilson v_, Feb 17 2017 *)
%o A282538 (PARI) isok(n) = (n%2) && vecmax(factor(n^2+4)[,1]) < n; \\ _Michel Marcus_, Feb 18 2017
%Y A282538 Cf. A256011 (generated similarly, but for n^2+1 instead of n^2+4).
%K A282538 nonn
%O A282538 1,1
%A A282538 _Michael Kaltman_, Feb 17 2017
%E A282538 a(22) onward from _Robert G. Wilson v_, Feb 17 2017