%I A114200
%S A114200 24,120,240,840,840,720,2520,1320,5280,6240,9360,3960,10920,3360,18480,
%T A114200 14280,24400,17160,6840,31920,10920,26520,43680,50160,16320,35880,57960,
%U A114200 73920,38760,15600,46200,100800,107640,122400,138600,128520,148200
%N A114200 When the n-th term of this sequence is added to or subtracted from the 
               n-th prime of the form 4k + 1 (i.e. A002144(n)), the result in both 
               cases is a square.
%C A114200 This sequence and A002144 give rise to a class of monic polynomials x^2 
               + bx + c where b = +/-A002144(n) and c = +/-a(n)/4 that will factor 
               over the integers regardless of the sign of c. For example, x^2 - 
               13x - 30 and x^2 - 13x + 30 are two such polynomials. Further polynomials 
               with this property can be found by transforming the roots.
%e A114200 a(2) = 120 and A002144(2)=13. 13^2 - 120 = 7^2 and 13^2 + 120 = 17^2.
%Y A114200 Cf. A002144.
%Y A114200 Sequence in context: A124952 A126411 A137799 this_sequence A069074 A059775 
               A052762
%Y A114200 Adjacent sequences: A114197 A114198 A114199 this_sequence A114201 A114202 
               A114203
%K A114200 nonn
%O A114200 1,1
%A A114200 Owen Mertens (owenmertens(AT)missouristate.edu), Nov 16 2005