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A065119 n-th cyclotomic polynomial is a trinomial. 9
3, 6, 9, 12, 18, 24, 27, 36, 48, 54, 72, 81, 96, 108, 144, 162, 192, 216, 243, 288, 324, 384, 432, 486, 576, 648, 729, 768, 864, 972, 1152, 1296, 1458, 1536, 1728, 1944, 2187, 2304, 2592, 2916, 3072, 3456, 3888, 4374, 4608, 5184, 5832, 6144, 6561, 6912, 7776, 8748, 9216 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Appears to be numbers of form 2^a * 3^b, a >= 0, b > 0. - Lekraj Beedassy, Sep 10 2004

This is true: see link "Cyclotomic trinomials". - Robert Israel, Jul 14 2015

REFERENCES

J.-M. De Koninck & A. Mercier, 1001 Problemes en Theorie Classique Des Nombres, Problem 733 pp. 74;310 Ellipses Paris 2004.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

Robert Israel, Cyclotomic trinomials

FORMULA

A206787(a(n)) = 4. - Reinhard Zumkeller, Feb 12 2012

a(n) = A033845(n)/2 = 3 * A003586(n). - Robert Israel, Jul 14 2015

EXAMPLE

The 54th cyclotomic polynomial is x^18 - x^9 + 1 which is trinomial, so 54 is in the sequence.

MAPLE

with(numtheory): a := []; for m from 1 to 3000 do if nops([coeffs(cyclotomic(m, x))])=3 then a := [op(a), m] fi od; print(a);

MATHEMATICA

max = 5000; Sort[Flatten[Table[2^a 3^b, {a, 0, Floor[Log[2, max]]}, {b, Floor[Log[3, max/2^a]]}]]] (* Alonso del Arte, May 19 2016 *)

PROG

(PARI) isok(n)=my(vp = Vec(polcyclo(n))); sum(k=1, #vp, vp[k] != 0) == 3; \\ Michel Marcus, Jul 11 2015

(PARI) list(lim)=my(v=List(), N); for(n=1, logint(lim\1, 3), N=3^n; while(N<=lim, listput(v, N); N<<=1)); Set(v) \\ Charles R Greathouse IV, Aug 07 2015

CROSSREFS

Differs at the 18th term from A063996.

Cf. A003586, A033845, A206787.

Sequence in context: A052287 A156997 A063996 * A293396 A173195 A232920

Adjacent sequences:  A065116 A065117 A065118 * A065120 A065121 A065122

KEYWORD

nonn

AUTHOR

Len Smiley, Nov 12 2001

EXTENSIONS

Offset set to 1 and more terms from Michel Marcus, Jul 11 2015

STATUS

approved

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Last modified November 19 14:52 EST 2018. Contains 317352 sequences. (Running on oeis4.)