A179210 a(n) is the smallest prime q such that (r-q)/(q-p) = n, where p<q<r are consecutive primes (or 0 if no such prime exists).

5, 3, 31, 8123, 139, 199, 45439, 1933, 523, 156157, 1951, 1669, 480209, 2971, 7759, 2181737, 12163, 28351, 6012899, 20809, 16141, 3933599, 163063, 86629, 13626257, 25471, 40639, 60487759, 79699, 149629, 217795247, 625699, 552403

Offset

1,1

Comments

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

It appears that a(3n+1) is greater than either a(3n) or a(3n+2). - Vladimir Shevelev and Robert G. Wilson v, Oct 20 2016

Links

Vladimir Shevelev and Robert G. Wilson v, Table of n, a(n) for n = 1..69

Formula

a(n) = nextprime(A181994(n)). - Robert G. Wilson v, Dec 23 2016

Mathematica

p = 2; q = 3; r = 5; t[_] = 0; While[p < 10^9, If[ Mod[r - q, q - p] == 0 && t[(r - q)/(q - p)] == 0, t[(r - q)/(q - p)] = q; Print[{(r - q)/(q - p), q}]]; p = q; q = r; r = NextPrime@ r]; t /@ Range @ 40 (* Robert G. Wilson v, Dec 11 2016 *)
Table[SelectFirst[Partition[Prime[Range[12010000]], 3, 1], Differences[#][[2]]/ Differences[#][[1]]==n&], {n, 33}][[All, 2]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 05 2018 *)

Prog

(PARI) a(n) = forprime(q=3, , my(p=precprime(q-1), r=nextprime(q+1)); if((r-q)/(q-p)==n, return(q))) \\ Felix Fröhlich, Dec 06 2018

Crossrefs

For records see A278574.

Cf. A001223, A179256, A181994.

Sequence in context: A324499 A189747 A279066 * A291843 A187278 A288184

Adjacent sequences: A179207 A179208 A179209 * A179211 A179212 A179213

Keyword

nonn

Author

Vladimir Shevelev, Jan 05 2011

Status

approved