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Search: id:A129515
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| A129515 |
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Numbers n such that binomial(2n,n) has the same prime factors as binomial(2k,k) for some k>n. |
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| 87, 199, 237, 467, 607, 967, 1127, 1319, 1483, 1903, 1943, 2012, 2047, 2287, 2348, 2359, 2464, 2479, 2495, 2507, 2623, 2645, 2719, 3349, 3467, 3514, 3568, 3629, 3633, 3712, 3847, 3919, 4088, 4224, 4287, 4360, 4479, 4927, 4987, 5087, 5167, 5224, 5669
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OFFSET
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1,1
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COMMENT
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The Erdos paper mentions 87 and 607. The paper conjectures that the sequence is infinite. For the n listed here, k=n+1. Note that we need only examine k such that pi(2n) = pi(2k), where pi is the prime counting function.
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REFERENCES
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P. Erdos, R. L. Graham, I. Z. Russa and E. G. Straus, On the prime factors of C(2n,n), Math. Comp. 29 (1975), 83-92.
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MATHEMATICA
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s={}; nLst={}; t={}; Do[p=Transpose[FactorInteger[Binomial[2n, n]]][[1]]; If[s!={} && p[[ -1]]!=s[[ -1, -1]], s={}; nLst={}]; pos=Position[s, p, 1, 1]; If[pos!={}, m=pos[[1, 1]]; AppendTo[t, nLst[[m]]], AppendTo[s, p]; AppendTo[nLst, n]], {n, 10000}]; t
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CROSSREFS
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Cf. A067434 (number of distinct prime factors in binomial(2n, n)).
Sequence in context: A063349 A101259 A063336 this_sequence A133524 A020314 A008899
Adjacent sequences: A129512 A129513 A129514 this_sequence A129516 A129517 A129518
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Apr 18 2007
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