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A280244
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Lexicographically ordered list of sequences that meet the criteria for R. L. Graham's sequence: k = a_1 < a_2 < ... < a_t = A006255(k) and a_1*a_2*...*a_t is a square.
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2
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1, 2, 3, 4, 6, 2, 3, 6, 3, 4, 6, 8, 3, 6, 8, 4, 5, 8, 9, 10, 5, 8, 10, 6, 8, 9, 12, 6, 8, 12, 7, 8, 9, 14, 7, 8, 14, 8, 9, 10, 12, 15, 8, 10, 12, 15, 9, 10, 12, 15, 16, 18, 10, 12, 15, 18, 11, 12, 14, 16, 21, 22, 11, 12, 14, 21, 22, 11, 12, 15, 16, 18, 20, 22
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OFFSET
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1,2
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COMMENTS
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LINKS
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EXAMPLE
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[8,9,10,12,15] appears as a row in the table because A006255(8) = 15 and the product of the row is a square: 8*9*10*12*15 = 360^2.
Table begins:
1;
2, 3, 4, 6;
2, 3, 6;
3, 4, 6, 8;
3, 6, 8;
4;
5, 8, 9, 10;
5, 8, 10;
6, 8, 9, 12;
6, 8, 12;
7, 8, 9, 14;
7, 8, 14;
8, 9, 10, 12, 15;
8, 10, 12, 15;
...
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MATHEMATICA
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MapIndexed[With[{b = #1, a = First@ #2}, Reverse@ Select[Rest@ Subsets@ Range[a, b], And[SubsetQ[#, {a, b}], IntegerQ@ Sqrt[Times @@ #]] &]] &, #] &@ Table[k = 0; Which[IntegerQ@ Sqrt@ n, k, And[PrimeQ@ n, n > 3], k = n, True, While[Length@ Select[n Map[Times @@ # &, n + Rest@ Subsets@ Range@ k], IntegerQ@ Sqrt@# &] == 0, k++]]; k + n, {n, 16}] // Flatten (* Michael De Vlieger, Dec 30 2016 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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