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A099490
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Least k such that the interval [n,k] contains a subset of integers whose product is twice a square.
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0
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2, 2, 6, 8, 8, 8, 8, 8, 15, 15, 18, 18, 18, 18, 18, 18, 18, 18, 27, 27, 27, 27, 27, 27, 32, 32, 32, 32, 32, 32, 32, 32, 45, 45, 45, 45, 45, 45, 45, 45, 50, 50, 50, 50, 50, 50, 50, 50, 50, 50, 63, 63, 63, 63, 63, 63, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72, 72
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OFFSET
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1,1
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LINKS
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Table of n, a(n) for n=1..72.
Andrew Granville and John Selfridge, Product of integers in an interval, modulo squares (pdf), Electronic Journal of Combinatorics, Volume 8(1), 2001.
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EXAMPLE
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a(9) = 15 because the interval [9,15] contains the subset {10,12,15} whose product is 2*30^2 and no shorter interval starting with 9 has such a subset.
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MATHEMATICA
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Needs["DiscreteMath`Combinatorica`"]; Table[If[n==1, n1=2, n1=n]; found=False; While[ !found, lst=Range[n, n1]; x=Times@@lst; {p, e}=Transpose[FactorInteger[x]]; Do[If[e[[i]]==1 && p[[i]]!=2, lst=DeleteCases[lst, _?(Mod[ #, p[[i]]]==0&)]], {i, Length[p]}]; i=1; While[i<2^Length[lst] && !found, ss=NthSubset[i, lst]; x=Times@@ss; If[Mod[x, 2]==0 && IntegerQ[Sqrt[x/2]], found=True (*; Print[{n, ss}]*)]; i++ ]; If[ !found, n1++ ]]; n1, {n, 100}]
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CROSSREFS
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Cf. A099500, A099501.
Sequence in context: A116542 A142243 A091441 * A167878 A033724 A033748
Adjacent sequences: A099487 A099488 A099489 * A099491 A099492 A099493
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe, Oct 19 2004
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STATUS
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approved
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