A168253 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).

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

Offset

1,1

Comments

Conjecture: a(n)>0 for all n.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..127

Mathematica

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 *)

Crossrefs

Cf. A179210, A179234, A001223

Sequence in context: A283507 A290074 A146317 * A357756 A181351 A266385

Adjacent sequences: A168250 A168251 A168252 * A168254 A168255 A168256

Keyword

nonn

Author

Vladimir Shevelev, Jan 05 2011

Status

approved