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, 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

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-François 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