The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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 Robert G. Wilson v, Table of n, a(n) for n = 1..123 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 Cf. A001223, A168253, A179210, A279067. Sequence in context: A293010 A236467 A328550 * A338051 A009183 A165893 Adjacent sequences: A179231 A179232 A179233 * A179235 A179236 A179237 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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