cp's OEIS Frontend

A242488 Triangle read by rows in which row n lists numbers k such that the greatest prime factor of k^2 - 2 is A038873(n), the n-th prime not congruent to 3 or 5 mod 8.

%I A242488 #24 Dec 22 2024 23:56:33
%S A242488 2,3,4,10,6,11,45,108,5,18,28,74,156,235,8,23,39,116,1201,17,24,58,
%T A242488 147,304,550,2272,390050,7,40,54,87,101,181,557,1558,43764,314766,12,
%U A242488 59,130,225,414,1077,1124,2686,3420,4035,32,41,178,333,698,844,1638,4567,15362,364384
%N A242488 Triangle read by rows in which row n lists numbers k such that the greatest prime factor of k^2 - 2 is A038873(n), the n-th prime not congruent to 3 or 5 mod 8.
%C A242488 From _Andrew Howroyd_, Dec 22 2024: (Start)
%C A242488 For any prime p, there are finitely many x such that x^2 - 2 has p as its largest prime factor.
%C A242488 The Filip Najman data file gives all 537 numbers x such that x^2 - 2 has no prime factor greater than 199. This includes a value for x = 1 which is not included here. (End)
%H A242488 Andrew Howroyd, <a href="/A242488/b242488.txt">Table of n, a(n) for n = 1..536</a> (first 21 rows for primes up to 199)
%H A242488 Filip Najman, <a href="http://web.math.hr/~fnajman/smooth.pdf">Smooth values of some quadratic polynomials</a>, Glasnik Matematicki Series III 45 (2010), pp. 347-355.
%H A242488 Filip Najman, <a href="https://web.math.pmf.unizg.hr/~fnajman/publications.html">List of Publications Page</a> (Adjacent to entry number 7 are links with a data file for the first 21 rows of this sequence).
%e A242488 Triangle of numbers k such that p is the greatest prime factor of k^2 - 2:
%e A242488 p\k  |  1 |  2 |  3  |  4  |  5   |  6   |  7   |  >= 8
%e A242488 ------------------------------------------------------------------------
%e A242488    2 |  2 |    |     |     |      |      |      |
%e A242488    7 |  3 |  4 |  10 |     |      |      |      |
%e A242488   17 |  6 | 11 |  45 | 108 |      |      |      |
%e A242488   23 |  5 | 18 |  28 |  74 |  156 |  235 |      |
%e A242488   31 |  8 | 23 |  39 | 116 | 1201 |      |      |
%e A242488   41 | 17 | 24 |  58 | 147 |  304 |  550 | 2272 | 390050;
%e A242488   47 |  7 | 40 |  54 |  87 |  101 |  181 |  557 | 1558, 43764, 314766;
%e A242488   71 | 12 | 59 | 130 | 225 |  414 | 1077 | 1124 | 2686, 3420, 4035;
%e A242488   73 | 32 | 41 | 178 | 333 |  698 |  844 | 1638 | 4567, 15362, 364384;
%e A242488   ...
%e A242488 6 is a term of row 3 because (6^2 - 2)/17 = 2 and 2 < 17;
%e A242488 11 is a term of row 3 because (11^2 - 2)/17 = 7 and 7 < 17;
%e A242488 45 is a term of row 3 because (45^2 - 2)/17^2 = 7 and 7 < 17;
%e A242488 108 is a term of row 3 because (108^2 - 2)/17 = 686 = 2*7^3 and 7 < 17.
%Y A242488 Cf. A038873, A164314, A059770 (first terms for n>1), A185396 (last terms), A379348 (row lengths).
%Y A242488 Cf. A223701.
%K A242488 nonn,tabf
%O A242488 1,1
%A A242488 _Juri-Stepan Gerasimov_, May 16 2014
%E A242488 Converted to triangle by _Andrew Howroyd_, Dec 22 2024