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%I #19 May 23 2024 06:29:52
%S 3,15,165,2145,40755,1181895,43730115,2317696095,136744069605,
%T 8341388245905,558873012475635,46386460035477705,4685032463583248205,
%U 501298473603407557935,65670100042046390089485,9128143905844448222438415,1360093441970822785143323835,221695231041244113978361785105
%N Partial products of primes with primitive root 2.
%C The poster by Arnold and Monagan reports that the cyclotomic polynomial of order a(6) is the first cyclotomic polynomial whose height is greater than its order. They also report the height of the cyclotomic polynomial Phi(a(7),x) is greater than the order squared. It is also true that k = a(5) is the least order such that the height of Phi(k,x) is greater than the square root of the order. - _T. D. Noe_, Apr 22 2008
%C Partial products of A001122. - _Charles R Greathouse IV_, Jun 21 2013
%H Andrew Arnold and Michael Monagan, <a href="http://www.cecm.sfu.ca/research/posters/arnold07.pdf">The Height of the 3,234,846,615th Cyclotomic Polynomial is Big (2,888,582,082,500,892,851)</a>.
%e 3 is the first prime with primitive root 2, so a(1) = 3.
%e 5 is the second prime with primitive root 2, so a(2) = 3*5 = 15.
%e 11 is the third prime with primitive root 2, so a(3) = 3*5*11 = 165.
%t FoldList[Times, Select[Prime[Range[40]], PrimitiveRoot[#] == 2 &]] (* _Amiram Eldar_, May 23 2024 *)
%Y Cf. A001122.
%K nonn
%O 1,1
%A Douglas Stones (dssto1(AT)student.monash.edu.au), Jul 27 2005
%E More terms from _Amiram Eldar_, May 23 2024