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A345020
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a(0) = a(1) = 1, a(n) = largest natural number m <= a(n-1) + a(n-2) where gcd(m,a(k)) = 1 for all 1 < k <= n-1.
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1
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1, 1, 2, 3, 5, 7, 11, 17, 23, 37, 59, 89, 139, 227, 361, 587, 947, 1531, 2477, 4007, 6481, 10487, 16963, 27449, 44393, 71837, 116227, 188063, 304289, 492343, 796627, 1288967, 2085593, 3374557, 5460139, 8834689, 14294827, 23129507, 37424333, 60553837, 97978169
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OFFSET
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0,3
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COMMENTS
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First differs from A055500 at a(14).
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LINKS
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EXAMPLE
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a(5) = 7 because 7 is the largest number less than or equal to a(4) + a(3) = 8 which is coprime to all the previous terms of sequence.
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MATHEMATICA
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a[0] = a[1] = 1; a[n_] := a[n] = Module[{k = a[n - 1] + a[n - 2]}, While[! AllTrue[Range[2, n - 2], CoprimeQ[a[#], k] &], k--]; k]; Array[a, 50, 0] (* Amiram Eldar, Jun 05 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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