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A179234
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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 (r-q)/(q-p) has denominator n in lowest terms.
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7
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3, 11, 29, 367, 149, 521, 127, 1847, 1087, 1657, 1151, 4201, 2503, 2999, 5779, 10831, 1361, 9587, 30631, 19373, 16183, 36433, 81509, 28277, 31957, 25523, 40343, 82129, 44351, 102761, 34123, 89753, 282559, 134581, 173429, 705389, 404671, 212777, 371027, 1060861, 265703, 461801, 156007, 544367, 576881, 927961, 1101071, 1904407, 604171, 396833
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OFFSET
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1,1
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COMMENTS
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The conjecture that a(n) exists for every n is a weaker conjecture than a related one in the comment to A179210.
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LINKS
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Table of n, a(n) for n=1..50.
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EXAMPLE
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For q=3 we have (r-q)/(q-p)=2/1. Therefore, a(1)=3.
For q=5: (r-q)/(q-p) = 1/1; for q = 7: (r-q)/(q-p) = 2/1; for q = 11: (r-q)/(q-p) = 1/2. Therefore, a(2)=11.
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MATHEMATICA
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f[n_] := Block[{p = 2, q = 3, r = 5}, While[ Denominator[(r - q)/(q - p)] != n, p = q; q = r; r = NextPrime@ r]; q]; Array[f, 50]
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PROG
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(PARI) a(n)=my(p=2, q=3); forprime(r=5, default(primelimit), if(denominator((r-q)/(q-p))==n, return(q)); p=q; q=r)
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CROSSREFS
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Cf. A179210, A001223.
Sequence in context: A000251 A159229 A122023 * A009183 A165893 A106397
Adjacent sequences: A179231 A179232 A179233 * A179235 A179236 A179237
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KEYWORD
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nonn,changed
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AUTHOR
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Vladimir Shevelev, Jan 05 2011
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EXTENSIONS
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Revised definition, new program, and terms past a(5) from Charles R Greathouse IV, Jan 12 2011.
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STATUS
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approved
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