login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A274908 Largest prime factor of 8^n - 1. 7

%I #38 Feb 25 2023 17:11:37

%S 7,7,73,13,151,73,337,241,262657,331,599479,109,121369,5419,23311,673,

%T 131071,262657,1212847,1321,649657,599479,10052678938039,38737,

%U 10567201,22366891,97685839,14449,9857737155463,18837001,658812288653553079,22253377

%N Largest prime factor of 8^n - 1.

%H <a href="/A274908/b274908.txt">Table of n, a(n) for n = 1..500</a>

%H J. Brillhart et al., <a href="http://dx.doi.org/10.1090/conm/022">Factorizations of b^n +- 1</a>, Contemporary Mathematics, Vol. 22, Amer. Math. Soc., Providence, RI, 3rd edition, 2002.

%F a(n) = A006530(A024088(n)). - _Michel Marcus_, Jul 11 2016

%F a(n) = A005420(3*n). - _Robert Israel_, Jul 12 2016

%e 8^5 -1 = 32767 = 7*31*151, so a(5) = 151.

%p f:= n -> max(map(t -> max(numtheory:-factorset(subs(x=2,t[1]))), factors(x^(3*n)-1)[2])):

%p map(f, [$1..120]); # _Robert Israel_, Jul 12 2016

%t Table[FactorInteger[8^n - 1][[-1, 1]], {n, 40}]

%o (Magma) [Maximum(PrimeDivisors(8^n-1)): n in [1..40]];

%Y Cf. A005420, A006530, A024088, A274905.

%Y Cf. similar sequences listed in A274906.

%K nonn

%O 1,1

%A _Vincenzo Librandi_, Jul 11 2016

%E Terms to a(100) in b-file from _Vincenzo Librandi_, Jul 13 2016

%E a(101)-a(402) in b-file from _Amiram Eldar_, Feb 02 2020

%E a(403)-a(500) in b-file from _Max Alekseyev_, Apr 25 2022, Sep 11 2022, Dec 05 2022, Feb 25 2023

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:02 EDT 2024. Contains 371235 sequences. (Running on oeis4.)