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A226833
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Triangle whose n-th row has the smallest n semiprimes in an arithmetic progression.
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4
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4, 4, 6, 6, 10, 14, 10, 22, 34, 46, 10, 22, 34, 46, 58, 201, 205, 209, 213, 217, 221, 133, 185, 237, 289, 341, 393, 445, 133, 185, 237, 289, 341, 393, 445, 497, 635, 707, 779, 851, 923, 995, 1067, 1139, 1211, 697, 793, 889, 985, 1081, 1177, 1273, 1369, 1465, 1561
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OFFSET
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1,1
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COMMENTS
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The largest term of each row is as small as possible. Although Nowicki reports on the 28th row of this triangle, those terms are too large. Sequence A096003 reports the largest terms.
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LINKS
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EXAMPLE
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Triangle:
4,
4, 6,
6, 10, 14,
10, 22, 34, 46,
10, 22, 34, 46, 58,
201, 205, 209, 213, 217, 221,
133, 185, 237, 289, 341, 393, 445,
133, 185, 237, 289, 341, 393, 445, 497,
635, 707, 779, 851, 923, 995, 1067, 1139, 1211,
697, 793, 889, 985, 1081, 1177, 1273, 1369, 1465, 1561
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MATHEMATICA
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SemiPrimeQ[n_Integer] := If[Abs[n] < 2, False, (2 == Plus @@ Transpose[FactorInteger[Abs[n]]][[2]])]; p2 = Select[Range[2000], SemiPrimeQ]; nn = Length[p2]; t = {}; n = 0; last = 1; While[n++; found = False; last = n; While[k = last - 1; While[d = p2[[last]] - p2[[k]]; nums = Table[p2[[last]] - i*d, {i, 0, n - 1}]; int = Intersection[nums, Take[p2, last]]; nums[[-1]] > 0 && Length[int] < n, k--]; nums[[-1]] <= 0 && last < nn, last++]; If[last < nn, AppendTo[t, Reverse[nums]]]; last < nn]; t
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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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