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A242488 Numbers n such that the largest prime factor of n^2 - 2 is 17. 4
6, 11, 45, 108 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 22 18:06 EST 2019. Contains 319365 sequences. (Running on oeis4.)