A179210 a(n) is the smallest prime q such that (r-q)/(q-p) = n, where p

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

Author

Vladimir Shevelev, Jan 05 2011

Keywords

• nonn

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

Crossrefs

For records see A278574.

Cf. A001223, A179256, A181994.

Programs

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 *)

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

Formula

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