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

1,1

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

Links

Table of n, a(n) for n=1..18.

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

Example

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.

Mathematica

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

Crossrefs

Cf. A001122.

Sequence in context: A304998 A105611 A329557 * A097489 A080696 A015013

Adjacent sequences: A108972 A108973 A108974 * A108976 A108977 A108978

Keyword

nonn

Author

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

Extensions

More terms from Amiram Eldar, May 23 2024

Status

approved