cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A085459 Numbers k such that k-th cyclotomic polynomial has exactly 3 positive coefficients.

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%I A085459 #21 Feb 23 2024 07:27:44
%S A085459 3,9,10,20,27,40,50,80,81,100,160,200,243,250,320,400,500,640,729,800,
%T A085459 1000,1250,1280,1600,2000,2187,2500,2560,3200,4000,5000,5120,6250,
%U A085459 6400,6561,8000,10000,10240,12500,12800,16000,19683,20000,20480,25000,25600
%N A085459 Numbers k such that k-th cyclotomic polynomial has exactly 3 positive coefficients.
%C A085459 Sequence appears to consist of 3^i, i > 0; and 2^i*5^j, i, j > 0. Are there any other terms? - _David Wasserman_, Feb 01 2005
%e A085459 9 is a member because the 9th cyclotomic polynomial is P(x) = x^6+x^3+1.
%t A085459 Select[Range@ 5000, Count[CoefficientList[Cyclotomic[#, x], x], _?(# > 0 &)] == 3 &] (* _Michael De Vlieger_, Oct 26 2017 *)
%o A085459 (PARI) n = 0; while (1, n++; p = polcyclo(n, x); d = poldegree(p); c = 0; i = 0; while (c < 4 && i <= d, if (polcoeff(p, i) > 0, c++); i++); if (c == 3, print(n))); \\ _David Wasserman_, Feb 01 2005
%Y A085459 Cf. A065119, A086765.
%K A085459 nonn,easy
%O A085459 1,1
%A A085459 Yuval Dekel (dekelyuval(AT)hotmail.com), Aug 14 2003
%E A085459 More terms from _David Wasserman_, Feb 01 2005