cp's OEIS Frontend

A223701 Irregular triangle of numbers k such that prime(n) is the largest prime factor of k^2 - 1.

%I A223701 #14 Dec 21 2024 15:26:08
%S A223701 3,2,5,7,17,4,9,11,19,26,31,49,161,6,8,13,15,29,41,55,71,97,99,127,
%T A223701 244,251,449,4801,8749,10,21,23,34,43,65,76,89,109,111,197,199,241,
%U A223701 351,485,769,881,1079,6049,19601,12,14,25,27,51,53,64,79,129,131,155
%N A223701 Irregular triangle of numbers k such that prime(n) is the largest prime factor of k^2 - 1.
%C A223701 Note that the first number of each row forms the sequence 3, 2, 4, 6, 10, 12,..., which is A039915. The first 25 rows, except the first, are in A181447-A181470.
%H A223701 Andrew Howroyd, <a href="/A223701/b223701.txt">Table of n, a(n) for n = 1..16223</a> (first 25 rows for primes up to 97)
%H A223701 Florian Luca and Filip Najman, <a href="https://arxiv.org/abs/1005.1533">On the largest prime factor of x^2-1</a>, arXiv:1005.1533 [math.NT], 2010.
%H A223701 Florian Luca and Filip Najman, <a href="https://doi.org/10.1090/S0025-5718-2010-02381-6">On the largest prime factor of x^2-1</a>, Mathematics of Computation 80 (2011), 429-435. (Paper has errata that was posted on the MOC website.)
%H A223701 Filip Najman, <a href="https://web.math.pmf.unizg.hr/~fnajman/publications.html">List of Publications Page</a> (Adjacent to entry number 4 are links with the data files for the first 25 rows (=16223 terms) of this sequence)
%e A223701 Irregular triangle:
%e A223701   {3},
%e A223701   {2, 5, 7, 17},
%e A223701   {4, 9, 11, 19, 26, 31, 49, 161},
%e A223701   {6, 8, 13, 15, 29, 41, 55, 71, 97, 99, 127, 244, 251, 449, 4801, 8749}
%t A223701 t = Table[FactorInteger[n^2 - 1][[-1,1]], {n, 2, 10^5}]; Table[1 + Flatten[Position[t, Prime[n]]], {n, 6}]
%Y A223701 Rows 2..25 with complete data are: A181447, A181448, A181449, A181450, A181451, A181452, A181453, A181454, A181455, A181456, A181457, A181458, A181459, A181460, A181461, A181462, A181463, A181464, A181465, A181466, A181467, A181468, A181469, A181470.
%Y A223701 Row 26 is A181568.
%Y A223701 Cf. A039915 (first terms), A175607 (last terms), A181471 (row lengths), A379344 (row sums).
%Y A223701 Cf. A223702, A223703, A223704 (related tables).
%K A223701 nonn,tabf
%O A223701 1,1
%A A223701 _T. D. Noe_, Apr 03 2013