A114735 - OEIS

%I #12 Apr 15 2017 05:22:06

%S 3,15,231,431985

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

%C 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?

%C 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]

%C 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

%H Andrew Arnold, Michael Monagan, <a href="http://dx.doi.org/10.1090/S0025-5718-2011-02467-1">Calculating cyclotomic polynomials</a>, Mathematics of Computation 80 (276) (2011) 2359-2379; <a href="http://www.cecm.sfu.ca/~ada26/cyclotomic/PDFs/CalcCycloPolysApr2010.pdf">preprint</a>.

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

%K nonn,more

%O 1,1

%A _T. D. Noe_, Mar 14 2006