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

Author

Vladimir Shevelev, Jan 05 2011

Keywords

• nonn

Comments

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

Links

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

Crossrefs

Cf. A179210, A179234, A001223

Programs

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 *)