A181568 Numbers k such that the largest prime factor of k^2-1 is 101.

100, 201, 203, 302, 304, 403, 405, 506, 607, 706, 807, 809, 1009, 1011, 1112, 1211, 1312, 1415, 1514, 1516, 1716, 1819, 1918, 2221, 2324, 2524, 2526, 2625, 2627, 3231, 3233, 3334, 3433, 3635, 3736, 3839, 4041, 4241, 4344, 4445, 4544, 4645, 4647, 4746

Offset: 1

Author

Klaus Brockhaus, Oct 31 2010

Keywords

• fini
• nonn

Comments

Sequence is finite, number of terms and last term are still unknown (cf. A175607, A181471).

From David A. Corneth, Sep 11 2019: (Start)

Are there any terms > 941747621709311?

As k^2 - 1 = (k - 1)(k + 1), a(n) is of the form 101*m +- 1. (End)

Links

• David A. Corneth, Table of n, a(n) for n = 1..3340 (first 2325 terms from Klaus Brockhaus, terms < 10^17).
• Florian Luca, Filip Najman, On the largest prime factor of x^2-1, arXiv:1005.1533 [math.NT], 2010.
• Florian Luca, 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.)

Crossrefs

Cf. A175607, A181471, A181447-A181470.

Programs

Magma

[ n: n in [2..5000] | m eq 101 where m is D[#D] where D is PrimeDivisors(n^2-1) ];

Mathematica

Select[Range[4746], FactorInteger[#^2-1][[-1, 1]]==101&] (* Metin Sariyar, Sep 15 2019 *)

PARI

is(n)=n=n^2-1; forprime(p=2, 97, n/=p^valuation(n, p)); n>1 && 101^valuation(n, 101)==n \\ Charles R Greathouse IV, Jul 01 2013