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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).
13
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.
Sequence in context: A324499 A189747 A279066 * A291843 A187278 A288184
KEYWORD
nonn
AUTHOR
Vladimir Shevelev, Jan 05 2011
STATUS
approved