OFFSET
3,1
COMMENTS
This is an extension of Cohn's irreducibility theorem, which is a(10) >= 9.
Brillhart, Filaseta, & Odlyzko show that a(n) >= n-1; Filaseta shows that 10^30 < a(10) < 62 * 10^30.
a(10) is due to Filaseta & Gross, a(8)-a(9) and a(11)-a(20) to Cole, and a(3)-a(7) to Dunn. Dunn proves that 7 <= a(2) <= 9, but its value is not known at present.
REFERENCES
J. Alexander. Irreducibility criteria for polynomials with non-negative integer coefficients. Master's Thesis, University of South Carolina. 1987. Cited in Dunn 2014.
LINKS
Charles R Greathouse IV, Table of n, a(n) for n = 3..20
J. Brillhart, M. Filaseta, and A. Odlyzko, On an irreducibility theorem of A. Cohn, Canad. J. Math. 33 (1981), pp. 1055-1059.
Morgan Cole, Sharp Bounds Associated With An Irreducibility Theorem For Polynomials Having Non-Negative Coefficients (2013).
Scott Michael Dunn, Explorations in Elementary and Analytic Number Theory (2014).
Michael Filaseta, Irreducibility criteria for polynomials with nonnegative coefficients, Canad. J. Math. 40 (1988), pp. 339-351.
Michael Filaseta and Samuel Gross, 49598666989151226098104244512918, J. Number Theory 137 (2014), pp. 16-49.
Wikipedia, Cohn's irreducibility criterion
CROSSREFS
KEYWORD
nonn,nice
AUTHOR
Charles R Greathouse IV, Sep 30 2015
STATUS
approved