Search: id:A159690
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%I A159690
%S A159690 841,881,925,4121,4405,4709,23885,25549,27329,139189,148889,159265,
%T A159690 811249,867785,928261,4728305,5057821,5410301,27558581,29479141,
%U A159690 31533545,160623181,171817025,183790969,936180505,1001423009,1071212269
%N A159690 Positive numbers y such that y^2 is of the form x^2+(x+881)^2 with integer 
               x.
%C A159690 (-41,a(1)) and (A130014(n), a(n+1)) are solutions (x, y) to the Diophantine 
               equation x^2+(x+881)^2 = y^2.
%C A159690 lim_{n -> infinity} a(n)/a(n-3) = 3+2*sqrt(2).
%C A159690 lim_{n -> infinity} a(n)/a(n-1) = (883+42*sqrt(2))/881 for n mod 3 = 
               {0, 2}.
%C A159690 lim_{n -> infinity} a(n)/a(n-1) = (2052963+1343918*sqrt(2))/881^2 for 
               n mod 3 = 1.
%F A159690 a(n) = 6*a(n-3)-a(n-6)for n > 6; a(1)=841, a(2)=881, a(3)=925, a(4)=4121, 
               a(5)=4405, a(6)=4709.
%F A159690 G.f.: (1-x)*(841+1722*x+2647*x^2+1722*x^3+841*x^4) / (1-6*x^3+x^6).
%F A159690 a(3*k-1) = 881*A001653(k) for k >= 1.
%e A159690 (-41, a(1)) = (-41, 841) is a solution: (-41)^2+(-41+881)^2 = 1681+705600 
               = 707281 = 841^2.
%e A159690 (A130014(1), a(2)) = (0, 881) is a solution: 0^2+(0+881)^2 = 776161 = 
               881^2.
%e A159690 (A130014(3), a(4)) = (2440, 4121) is a solution: 2440^2+(2440+881)^2 
               = 5953600+11029041 = 16982641 = 4121^2.
%o A159690 (PARI) {forstep(n=-44, 10000000, [3, 1], if(issquare(2*n^2+1762*n+776161, 
               &k), print1(k, ",")))}
%Y A159690 Cf. A130014, A001653, A156035 (decimal expansion of 3+2*sqrt(2)), A159691 
               (decimal expansion of (883+42*sqrt(2))/881), A159692 (decimal expansion 
               of (2052963+1343918*sqrt(2))/881^2).
%Y A159690 Sequence in context: A091036 A091038 A121498 this_sequence A108324 A133496 
               A121499
%Y A159690 Adjacent sequences: A159687 A159688 A159689 this_sequence A159691 A159692 
               A159693
%K A159690 nonn
%O A159690 1,1
%A A159690 Klaus Brockhaus (klaus-brockhaus(AT)t-online.de), Apr 21 2009

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