A179256 a(n) is the smallest prime q such that (q-p)/(r-q) = n, where p<q<r are consecutive primes (or 0 if none exist).

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

1,1

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

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 *)

Crossrefs

Cf. A179210, A179234, A168253, A001223

Sequence in context: A090119 A174922 A088484 * A209659 A266820 A335455

Adjacent sequences: A179253 A179254 A179255 * A179257 A179258 A179259

Keyword

nonn

Author

Vladimir Shevelev, Jan 05 2011

Status

approved