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 A178868 Numbers n such that the trinomial x^n + A x + B has an irreducible cubic as its lowest-degree factor (for some nonzero integers A,B). 2
 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 17, 22, 24, 52 (list; graph; refs; listen; history; text; internal format)
 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. LINKS EXAMPLE a(3)=8 because e.g. x^8+36x-13 has the cubic factor x^3-x^2+3x-1. CROSSREFS Sequence in context: A269801 A250048 A051053 * A069838 A067901 A115840 Adjacent sequences:  A178865 A178866 A178867 * A178869 A178870 A178871 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

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Last modified March 24 11:46 EDT 2019. Contains 321448 sequences. (Running on oeis4.)