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A168253
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a(n) is the smallest prime q such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator n (or 0, if such a prime does not exist).
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9
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5, 3, 23, 89, 139, 199, 113, 1933, 523, 3089, 1129, 1669, 2477, 2971, 4297, 5591, 1327, 28351, 30593, 19333, 16141, 36389, 81463, 28229, 31907, 19609, 35617, 82073, 44293, 102701, 34061, 288583, 221327, 134513, 173359, 360091
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OFFSET
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1,1
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COMMENTS
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Conjecture: a(n)>0 for all n.
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LINKS
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MATHEMATICA
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f[n_] := Block[{p = 2, q = 3, r = 5}, While[ Numerator[(r - q)/(q - p)] != n, p = q; q = r; r = NextPrime@ r]; q]; Array[f, 36]
p = 2; q = 3; r = 5; t[_] = 0; While[q < 100000000, If[ t[ Denominator[(q - p)/(r - q)]] == 0, t[ Denominator[(q - p)/(r - q)]] = q]; p = q; q = r; r = NextPrime@ r]; t@# & /@ Range@100 (* Robert G. Wilson v, Dec 11 2016 *)
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CROSSREFS
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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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