%I #29 Jan 12 2024 10:05:06

%S 1,4,8,9,11,16,25,27,31,32,36,41,44,49,61,71,72,81,88,99,100,101,108,

%T 121,124,125,128,131,144,151,164,169,176,181,191,196,200,211,216,225,

%U 241,243,244,248,251,256,271,275,279,281,284,288,289,297,311,324,328,331,341,343,352,361,369,392,396,400,401,404

%N Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^5/m) != 0.

%C Connect lines between the consecutive partial sums of Sum_{k=0..m-1} exp(2*Pi*i*k^5/m) != 0; this sequence gives values of m for which the resulting graph is "infinite."

%C A368959 is the intersection of all such sequences over exp(2*Pi*i*k^s/m), where s >= 2. Especially, all terms from A368959 are also here. - _Vaclav Kotesovec_, Jan 10 2024

%e 4 is a term because Sum_{k=0..3} exp(2*Pi*i*k^5/4) = 2 != 0.

%e 11 is a term because Sum_{k=0..10} exp(2*Pi*i*k^5/11) = 1 + 10*cos(2*Pi/11) != 0.

%e 12 is not a term because Sum_{k=0..11} exp(2*Pi*i*k^5/12) = 0.

%Y Cf. A001074, A042965 (Sum_{k=0..m-1} exp(2*Pi*i*k^(2n)/m) != 0 for all n>0).

%Y Cf. A368959.

%K easy,nonn

%O 1,2

%A _Kevin Ge_, Jan 06 2024