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A227727
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a(n) is the least r>=3 such that the difference between n and the nearest r-gonal number<=n is an r-gonal number.
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1
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3, 3, 3, 3, 3, 4, 3, 3, 4, 3, 3, 3, 5, 3, 7, 3, 3, 4, 3, 7, 4, 3, 3, 5, 3, 4, 4, 3, 3, 3, 11, 3, 16, 9, 3, 5, 3, 3, 19, 3, 4, 7, 3, 6, 22, 3, 3, 5, 3, 4, 4, 3, 5, 4, 19, 3, 3, 15, 3, 11, 6, 3, 7, 5, 4, 3, 3, 3, 4, 3, 5, 5, 3, 4, 37, 5, 3, 14, 3, 3, 4, 3, 4, 13
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OFFSET
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0,1
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COMMENTS
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The n-th r-gonal number is n((n-1)r-2(n-2))/2, such that 3-gonal numbers are triangular numbers, 4-gonal numbers are squares, etc.
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LINKS
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MATHEMATICA
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rGonalQ[r_, 0]:=True; rGonalQ[r_, n_]:=IntegerQ[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]; nthrGonal[r_, n_]:=(n (r-2)(n-1))/2+n; prevrGonal[r_, n_]:=nthrGonal[r, Floor[(Sqrt[((8r-16)n+(r-4)^2)]+r-4)/(2r-4)]]; (* previous r-gonal number greater than or equal to n *) Table[NestWhile[#+1&, 3, !rGonalQ[#, n-prevrGonal[#, n]]&], {n, 0, 99}] (* Peter J. C. Moses, Aug 03 2013 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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