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Search: id:A090956
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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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+0
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
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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a(n) > a(n-1), a(n) + a(n-1) is a square, a(n) - a(n-1) is square-free.
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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}] (Propper)
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CROSSREFS
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Cf. A090955.
Sequence in context: A057268 A085401 A085061 this_sequence A108972 A019097 A104264
Adjacent sequences: A090953 A090954 A090955 this_sequence A090957 A090958 A090959
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Dec 31 2003
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EXTENSIONS
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Corrected and extended by Ryan Propper (rpropper(AT)stanford.edu), Aug 27 2005
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