A223702 Irregular triangle of numbers k such that prime(n) is the largest prime factor of k^2 + 1.

1, 2, 3, 7, 5, 8, 18, 57, 239, 4, 13, 21, 38, 47, 268, 12, 17, 41, 70, 99, 157, 307, 6, 31, 43, 68, 117, 191, 302, 327, 882, 18543, 9, 32, 73, 132, 278, 378, 829, 993, 2943, 23, 30, 83, 182, 242, 401, 447, 606, 931, 1143, 1772, 6118, 34208, 44179, 85353, 485298

Offset

1,2

Comments

Note that primes of the form 4x+3 are not divisors.

Links

Table of n, a(n) for n=1..57.

Example

Irregular triangle:
{1},
{},
{2, 3, 7},
{},
{},
{5, 8, 18, 57, 239},
{4, 13, 21, 38, 47, 268},
{},
{},
{12, 17, 41, 70, 99, 157, 307},
{},
{6, 31, 43, 68, 117, 191, 302, 327, 882, 18543},
{9, 32, 73, 132, 278, 378, 829, 993, 2943}

Mathematica

t = Table[FactorInteger[n^2 + 1][[-1, 1]], {n, 10^5}]; Table[Flatten[Position[t, Prime[n]]], {n, 13}]

Crossrefs

Cf. A175607 (largest number k such that the greatest prime factor of k^2-1 is prime(n)).

Cf. A223701-A223707 (related sequences).

Sequence in context: A225403 A069786 A128804 * A120726 A060203 A131880

Adjacent sequences: A223699 A223700 A223701 * A223703 A223704 A223705

Keyword

nonn,tabf

Author

T. D. Noe, Apr 03 2013

Status

approved