A242488 Numbers m such that the largest prime factor of m^2 - 2 is 17.

6, 11, 45, 108

Offset

1,1

Comments

Irregular triangle of numbers k such that A038873(n) is the largest prime factor of k^2 - 2:

n\k| 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11

------------------------------------------------------------------------

1 | 2 | | | | | | | | | |

2 | 3 | 4 | 10 | | | | | | | |

3 | 6 | 11 | 45 | 108 | | | | | | |

4 | 5 | 18 | 28 | 74 | 156 | 235 | | | | |

5 | 8 | 23 | 39 | 116 | 1201 | | | | | |

6 | 17 | 24 | 58 | 147 | 304 | 550 | 2272 | | | |

7 | 7 | 40 | 54 | 87 | 101 | 181 | 557 | 1558 | | |

8 | 12 | 59 | 130 | 225 | 414 | 1077 | 1124 | 2686 | 3420 | 4035 |

9 | 32 | 41 | 178 | 333 | 698 | 844 | 1638 | 4567 | | |

10 | 9 | 70 | 88 | 228 | 386 | 465 | 623 | 878 | 1431 | 7654 | 9313

..., where A038873(n) = primes p such that x^2 = 2 has a solution mod p.

a(5) > 10^7. - Tom Edgar, May 16 2014

Links

Table of n, a(n) for n=1..4.

Example

6 is in this sequence because (6^2 - 2)/17 = 2 and 2 < 17;
11 is in this sequence because (11^2 - 2)/17 = 7 and 7 < 17;
45 is in this sequence because (45^2 - 2)/17^2 = 7 and 7 < 17;
108 is in this sequence because (108^2 - 2)/17 = 686 = 2*7^3 and 7 < 17.

Prog

(Magma) [n: n in [2..120] | k eq 17 where k is D[#D] where D is PrimeDivisors(n^2-2)];

Crossrefs

Cf. A223701.

Sequence in context: A270280 A270727 A216269 * A094555 A271056 A271255

Adjacent sequences: A242485 A242486 A242487 * A242489 A242490 A242491

Keyword

nonn

Author

Juri-Stepan Gerasimov, May 16 2014

Status

approved