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A090956
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Numbers in increasing order such that successive sums are squares and successive differences are squarefree.
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3
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1, 3, 6, 19, 30, 51, 70, 99, 157, 167, 233, 343, 386, 455, 506, 583, 642, 727, 794, 887, 1138, 1671, 1693, 1788, 1933, 2036, 2453, 2731, 2745, 3031, 3053, 3508, 3717, 4027, 4073, 4391, 4825, 4976, 5225, 5384, 5641, 5808, 6073, 6471, 6754, 6935, 7226, 7903
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OFFSET
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0,2
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COMMENTS
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a(n) > a(n-1), a(n) + a(n-1) is a square, a(n) - a(n-1) is squarefree.
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LINKS
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Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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EXAMPLE
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103 follows 93 as 103 - 93 = 10 is squarefree and 93 + 103 = 196 = 14^2.
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MATHEMATICA
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<<NumberTheory`; a = 1; Print[a]; Do[k = a + 1; While[ !(SquareFreeQ[k - a] && IntegerQ[Sqrt[k + a]]), k++ ]; a = k; Print[a], {n, 1, 100}] (* Ryan Propper, Aug 27 2005 *)
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CROSSREFS
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Cf. A090955.
Sequence in context: A085061 A294570 A306968 * A108972 A304965 A203797
Adjacent sequences: A090953 A090954 A090955 * A090957 A090958 A090959
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy, Dec 31 2003
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EXTENSIONS
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Corrected and extended by Ryan Propper, Aug 27 2005
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STATUS
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approved
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