A379350 Triangle read by rows in which row n lists numbers k such that the greatest prime factor of k^2 + 2 is A033203(n), the n-th prime not congruent to 5 or 7 mod 8.

0, 1, 2, 4, 5, 22, 3, 8, 14, 19, 140, 7, 10, 24, 41, 58, 265, 707, 6, 13, 25, 32, 44, 63, 146, 184, 602, 3407, 21362, 11, 30, 52, 71, 112, 194, 298, 481, 503, 2695, 3433, 4991, 16, 27, 59, 70, 102, 113, 317, 500, 586, 1048, 2951, 3424, 4972, 8240, 12658, 83834, 686210, 1306066

Offset

1,3

Comments

For any prime p, there are finitely many x such that x^2 + 2 has p as its greatest prime factor.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..915 (first 21 rows for primes up to 193)

Filip Najman, Smooth values of some quadratic polynomials, Glasnik Matematicki Series III 45 (2010), pp. 347-355.

Filip Najman, List of Publications Page (Adjacent to entry number 7 are links with a data file for rows 2..21 (=914 terms) of this sequence).

Example

Irregular triangle begins:
   p | {k}
-----+------------------
   2 | {0}
   3 | {1, 2, 4, 5, 22}
  11 | {3, 8, 14, 19, 140}
  17 | {7, 10, 24, 41, 58, 265, 707}
  19 | {6, 13, 25, 32, 44, 63, 146, 184, 602, 3407, 21362}
  41 | {11, 30, 52, 71, 112, 194, 298, 481, 503, 2695, 3433, 4991}
  ...

Crossrefs

Cf. A033203, A379351, A379352 (first terms), A185397 (last terms), A379349 (row lengths).

Cf. A223701, A223702, A242488.

Sequence in context: A101587 A277853 A200906 * A036986 A144420 A126667

Adjacent sequences: A379347 A379348 A379349 * A379351 A379352 A379353

Keyword

nonn,tabf

Author

Andrew Howroyd, Dec 22 2024

Status

approved