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A179328 a(n) is the smallest prime q > a(n-1) such that, for the previous prime p and the following prime r, the fraction (q-p)/(r-q) has denominator prime(n) (or 0, if such a prime does not exist). 3
3, 23, 139, 293, 1129, 2477, 8467, 30593, 81463, 85933, 190409, 404597, 535399, 840353, 1100977, 2127163, 4640599, 6613631, 6958667, 10343761, 24120233, 49269581, 83751121, 101649649, 166726367, 273469741, 310845683, 568951459 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

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

LINKS

Table of n, a(n) for n=1..28.

MAPLE

with(numtheory):

a:= proc(n) option remember; local k, p, q, r, pn;

      pn:= ithprime(n);

      for k from `if`(n=1, 1, pi(a(n-1))) do

        p:= ithprime(k);

        q:= ithprime(k+1);

        r:= ithprime(k+2);

        if denom((q-p)/(r-q)) = pn then break fi

      od; q

    end:

seq(a(n), n=1..10);  # Alois P. Heinz, Jan 06 2011

MATHEMATICA

a[n_] := a[n] = Module[{k, p, q, r, pn},

     pn = Prime[n];

     For[k = If[n == 1, 1, PrimePi[a[n - 1]]], True, k++,

     p = Prime[k];

     q = Prime[k + 1];

     r = Prime[k + 2];

     If [Denominator[(q - p)/(r - q)] == pn, Break[]]]; q];

Table[a[n], {n, 1, 10}] (* Jean-Fran├žois Alcover, Mar 18 2022, after Alois P. Heinz *)

CROSSREFS

Cf. A168253, A179210, A179234, A179240, A179256, A001223

Sequence in context: A196881 A049164 A081413 * A255952 A089950 A198797

Adjacent sequences:  A179325 A179326 A179327 * A179329 A179330 A179331

KEYWORD

nonn

AUTHOR

Vladimir Shevelev, Jan 06 2011

EXTENSIONS

More terms from Alois P. Heinz, Jan 06 2011

STATUS

approved

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Last modified July 4 16:26 EDT 2022. Contains 355081 sequences. (Running on oeis4.)