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A188891
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Least triangular n-gonal number greater than 1, or 0 if none exists.
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5
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3, 36, 210, 6, 55, 21, 325, 10, 0, 105, 36, 1275, 15, 45, 231, 0, 946, 276, 21, 11935, 66, 136, 351, 1596, 78, 28, 1225, 595, 820, 58653, 190, 325, 1335795, 36, 6670, 0, 561, 4005, 120, 1128, 1485, 203841, 45, 666, 6903, 465, 4950, 20910, 741, 153, 10731, 8911, 55, 1953
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OFFSET
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3,1
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COMMENTS
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See A188893 and A188894 for the corresponding indices of these terms. Note that a(n) is zero for n = 11, 18, 38 (numbers in A188892). Although the Mathematica program searches only the first 20000 triangular numbers for n-gonal numbers, the Reduce function can show that there are no triangular n-gonal numbers (other than 0 and 1) for these n.
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LINKS
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MATHEMATICA
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NgonIndex[n_, v_] := (-4 + n + Sqrt[16 - 8*n + n^2 - 16*v + 8*n*v])/(n - 2)/2; Table[k = 2; While[tr = k*(k+1)/2; i = NgonIndex[n, tr]; k < 20000 && ! IntegerQ[i], k++]; If[k==20000, tr=0]; tr, {n, 3, 50}]
Table[SelectFirst[PolygonalNumber[n, Range[2, 1000]], OddQ[Sqrt[8#+1]]&], {n, 3, 100}]/.Missing["NotFound"]->0 (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 10 2019 *)
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CROSSREFS
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Cf. A000217 (triangular numbers), A100252 (similar sequence for squares).
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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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