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%I #30 Sep 08 2022 08:45:54
%S 100,201,203,302,304,403,405,506,607,706,807,809,1009,1011,1112,1211,
%T 1312,1415,1514,1516,1716,1819,1918,2221,2324,2524,2526,2625,2627,
%U 3231,3233,3334,3433,3635,3736,3839,4041,4241,4344,4445,4544,4645,4647,4746
%N Numbers k such that the largest prime factor of k^2-1 is 101.
%C Sequence is finite, number of terms and last term are still unknown (cf. A175607, A181471).
%C From _David A. Corneth_, Sep 11 2019: (Start)
%C Are there any terms > 941747621709311?
%C As k^2 - 1 = (k - 1)(k + 1), a(n) is of the form 101*m +- 1. (End)
%H David A. Corneth, <a href="/A181568/b181568.txt">Table of n, a(n) for n = 1..3340</a> (first 2325 terms from Klaus Brockhaus, terms < 10^17).
%H Florian Luca, 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 Florian Luca, 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.)
%t Select[Range[4746], FactorInteger[#^2-1][[-1, 1]]==101&] (* _Metin Sariyar_, Sep 15 2019 *)
%o (Magma) [ n: n in [2..5000] | m eq 101 where m is D[#D] where D is PrimeDivisors(n^2-1) ];
%o (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
%Y Cf. A175607, A181471, A181447-A181470.
%K fini,nonn
%O 1,1
%A _Klaus Brockhaus_, Oct 31 2010
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