OFFSET
1,1
COMMENTS
a(1)=6 because e.g. x^6+16x+16 have factor x^3-2x^2+4
a(2)=7 because e.g. x^7-183352x+814800 have factor x^3+4x^2+22x-300
a(3)=8 because e.g. x^8+7x-4 have factor x^3-x^2+2x-1
a(4)=9 because e.g. x^9+2187x+2916 have factor x^3+3x^2+9x+9
a(5)=10 because e.g. x^10+297x-243 have factor x^3+3x-3 (*Schinzel*)
a(6)=12 because e.g. x^12+576x+368 have factor x^3+2x^2+4x+2 (*Browkin-Schinzel*)
a(7)=13 because e.g. x^13+768x+1024 have factor x^3+2x^2+4x+4 (*Browkin*)
a(8)=14 because x^14+4x+3 have factor x^3-x^2+1 (*Bremner*)
a(9)=15 because x^15-1059328125x+2378362500 have factor x^3+15x-45 (*Browkin*)
a(10)=16 because x^16+3486328125x+9277343750 have factor x^3+5x^2+25x+50 (*Bremner*)
a(11)=17 because x^17+103x+56 have factor x^3-x^2+x+1 (*Bremner*)
a(12)=22 because x^22+376832x-425984 have factor x^3+ 2 x^2-4 (*Browkin*)
a(13)=24 because x^24+14336x+12032 have factor x^3-2x^2+2 (*Browkin-Schinzel*)
a(14)=52 because x^52+2731599200256x+3539053051904 have factor x^3+2x^2+4x+4 (*Browkin*)
REFERENCES
Schinzel A. 1993. On reducible trinomials. Dissertationes Mathematicae. Warszawa Vol. CCCXXIX, pp.1-83.
Schinzel A. 2000. On reducible trinomials, II. Publicationes Mathematicae. Debrecen. Tomus 56 Fasc.3-4, pp.575-608.
EXAMPLE
a(3)=8 because e.g. x^8+36x-13 has the cubic factor x^3-x^2+3x-1.
CROSSREFS
KEYWORD
more,nonn
AUTHOR
Artur Jasinski, Jun 20 2010,Jun 24 2010
EXTENSIONS
Definition edited by N. J. A. Sloane, Jun 25 2010
11 inserted Artur Jasinski, Jun 25 2010
16 inserted and 11 deleted Artur Jasinski, Jun 29 2010
STATUS
approved