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A064765
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a(n) is the smallest number such that for, all m<n, both a(n)*a(m) and a(n)+a(m) are nonsquares.
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0
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1, 2, 5, 6, 12, 17, 21, 22, 26, 29, 33, 39, 40, 46, 51, 53, 56, 57, 66, 73, 77, 85, 86, 89, 97, 101, 102, 106, 114, 117, 131, 133, 134, 135, 137, 141, 146, 149, 151, 161, 165, 166, 176, 177, 181, 182, 197, 201, 202, 206, 209, 211, 214, 221, 229, 231, 237, 241, 246
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OFFSET
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1,2
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COMMENTS
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No number occurs more than once in the sequence because if a(n)=m then if m occurs again then a(n)*m=m^2. a(n) is always bigger than a(n-1) because all numbers less than a(n-1) have been checked to see if they make a square and if any do then because of the uniqueness of each value of a(n) then they must have already occurred in the sequence previously.
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LINKS
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EXAMPLE
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a(4) = 6 because a(1)*6 = 6, a(2)*6 = 12, a(3)*6 = 30 and a(1)+6 = 7, a(2)+6 = 8, a(3)+6=11, all nonsquares
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Jonathan Ayres (jonathan.ayres(AT)btinternet.com), Oct 18 2001
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STATUS
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approved
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