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

3, 2, 5, 7, 17, 4, 9, 11, 19, 26, 31, 49, 161, 6, 8, 13, 15, 29, 41, 55, 71, 97, 99, 127, 244, 251, 449, 4801, 8749, 10, 21, 23, 34, 43, 65, 76, 89, 109, 111, 197, 199, 241, 351, 485, 769, 881, 1079, 6049, 19601, 12, 14, 25, 27, 51, 53, 64, 79, 129, 131, 155

Offset

1,1

Comments

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.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..16223 (first 25 rows for primes up to 97)

Florian Luca and Filip Najman, On the largest prime factor of x^2-1, arXiv:1005.1533 [math.NT], 2010.

Florian Luca and Filip Najman, On the largest prime factor of x^2-1, Mathematics of Computation 80 (2011), 429-435. (Paper has errata that was posted on the MOC website.)

Filip Najman, List of Publications Page (Adjacent to entry number 4 are links with the data files for the first 25 rows (=16223 terms) of this sequence)

Example

Irregular triangle:
  {3},
  {2, 5, 7, 17},
  {4, 9, 11, 19, 26, 31, 49, 161},
  {6, 8, 13, 15, 29, 41, 55, 71, 97, 99, 127, 244, 251, 449, 4801, 8749}

Mathematica

t = Table[FactorInteger[n^2 - 1][[-1, 1]], {n, 2, 10^5}]; Table[1 + Flatten[Position[t, Prime[n]]], {n, 6}]

Crossrefs

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.

Row 26 is A181568.

Cf. A039915 (first terms), A175607 (last terms), A181471 (row lengths), A379344 (row sums).

Cf. A223702, A223703, A223704 (related tables).

Sequence in context: A350192 A239260 A013655 * A220519 A094894 A089334

Adjacent sequences: A223698 A223699 A223700 * A223702 A223703 A223704

Keyword

nonn,tabf

Author

T. D. Noe, Apr 03 2013

Status

approved