A108975 Partial products of primes with primitive root 2.

3, 15, 165, 2145, 40755, 1181895, 43730115, 2317696095, 136744069605, 8341388245905, 558873012475635, 46386460035477705, 4685032463583248205, 501298473603407557935, 65670100042046390089485, 9128143905844448222438415, 1360093441970822785143323835, 221695231041244113978361785105

Offset: 1

Author

Douglas Stones (dssto1(AT)student.monash.edu.au), Jul 27 2005

Keywords

• nonn

Comments

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

Partial products of A001122. - Charles R Greathouse IV, Jun 21 2013

Examples

			3 is the first prime with primitive root 2, so a(1) = 3.
5 is the second prime with primitive root 2, so a(2) = 3*5 = 15.
11 is the third prime with primitive root 2, so a(3) = 3*5*11 = 165.
		

Links

• Andrew Arnold and Michael Monagan, The Height of the 3,234,846,615th Cyclotomic Polynomial is Big (2,888,582,082,500,892,851).

Crossrefs

Cf. A001122.

Programs

Mathematica

FoldList[Times, Select[Prime[Range[40]], PrimitiveRoot[#] == 2 &]] (* Amiram Eldar, May 23 2024 *)

Extensions

More terms from Amiram Eldar, May 23 2024