A179256 a(n) is the smallest prime q such that (q-p)/(r-q) = n, where p

5, 11, 29, 6421, 149, 521, 84913, 1949, 1277, 43391, 1151, 4547, 933151, 2999, 6947, 1568867, 10007, 32297, 4131223, 25301, 78779, 12809491, 91079, 28277, 13626407, 35729, 117497, 37305881, 399851, 102761, 217795433, 288647, 296909, 240485461, 173429, 1026029, 213158501, 1053179, 371027, 1163010421, 1885151, 461801, 1661688551, 1155821, 576881, 3403741987, 4876607, 4252679, 10394432611, 838349, 1775171

Offset: 1

Author

Vladimir Shevelev, Jan 05 2011

Keywords

• nonn

Comments

Conjecture: a(n)>0 for n >= 1.

It would appear that a(3n+1) is greater than either a(3n) or a(3n+2).

Records appear for a(n) for n's: 1, 2, 3, 4, 7, 13, 16, 19, 22, 25, 28, 31, 34, 40, 43, 46, 49, ..., .

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..57

Crossrefs

Cf. A179210, A179234, A168253, A001223

Programs

Mathematica

f[n_] := f[n] = Block[{p = 3, q = 5, r = 7}, While[p + n*r != (n + 1) q, p = q; q = r; r = NextPrime@ r]; q]; Array[f, 33]
p = 2; q = 3; r = 5; t[] = 0; While[p < 10^9, If[ Mod[q - p, r - q] == 0 && t[(q - p)/(r - q)] == 0, t[(q - p)/(r - q)] = q; Print[{(q - p)/(r - q), q}]]; p = q; q = r; r = NextPrime@ r]; t@# & /@ Range@45 (* _Robert G. Wilson v, Dec 10 2016 *)