A114735 Least odd number k such that Phi(k,x) is a flat cyclotomic polynomial of order n.

3, 15, 231, 431985

Offset: 1

Author

T. D. Noe, Mar 14 2006

Keywords

• nonn
• more

Comments

A flat polynomial is defined to be a polynomial whose coefficients are -1, 0, or 1. Order n means that k is the product of n distinct odd primes. Although the first four numbers are triangular (A000217), this appears to be a coincidence. Are there flat cyclotomic polynomials of all orders?

Conjecture that the next two terms are 746443728915 = 3 * 5 * 31 * 929 * 1727939 and 7800513423460801052132265 = 3 * 5 * 31 * 929 * 1727941 * 10450224300389. [T. D. Noe, Apr 13 2010]

In 2010, Andrew Arnold reported to me that the order of 746443728915 is 3. His paper has details about how the computation was done. - T. D. Noe, Mar 20 2013

Links

• Andrew Arnold and Michael Monagan, Calculating cyclotomic polynomials, Mathematics of Computation 80 (276) (2011) 2359-2379; preprint.

Crossrefs

Cf. A117223 (third-order flat cyclotomic polynomials), A117318 (fourth-order flat cyclotomic polynomials).