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