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A179234 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. 10
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
The conjecture that a(n) exists for every n is a weaker conjecture than a related one in the comment to A179210.
LINKS
EXAMPLE
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.
MATHEMATICA
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]
p = 2; q = 3; r = 5; t[_] = 0; While[q < 100000000, If[ t[ Denominator[(r - q)/(q - p)]] == 0, t[ Denominator[(r - q)/(q - p)]] = q]; p = q; q = r; r = NextPrime@ r]; t@# & /@ Range@100 (* Robert G. Wilson v, Dec 11 2016 *)
PROG
(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)
CROSSREFS
Sequence in context: A293010 A236467 A328550 * A338051 A009183 A165893
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jan 05 2011
EXTENSIONS
Revised definition, new program, and terms past a(5) from Charles R Greathouse IV, Jan 12 2011
STATUS
approved

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Last modified July 18 11:13 EDT 2024. Contains 374378 sequences. (Running on oeis4.)