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.

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

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