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A114735
Least odd number k such that Phi(k,x) is a flat cyclotomic polynomial of order n.
0
3, 15, 231, 431985
OFFSET
1,1
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, 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).
Sequence in context: A303290 A298114 A301457 * A290970 A288987 A288986
KEYWORD
nonn,more
AUTHOR
T. D. Noe, Mar 14 2006
STATUS
approved