A368812 Numbers m such that Sum_{k=0..m-1} exp(2*Pi*i*k^5/m) != 0.

1, 4, 8, 9, 11, 16, 25, 27, 31, 32, 36, 41, 44, 49, 61, 71, 72, 81, 88, 99, 100, 101, 108, 121, 124, 125, 128, 131, 144, 151, 164, 169, 176, 181, 191, 196, 200, 211, 216, 225, 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

Offset: 1

Author

Kevin Ge, Jan 06 2024

Keywords

• easy
• nonn

Comments

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."

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

Examples

			4 is a term because Sum_{k=0..3} exp(2*Pi*i*k^5/4) = 2 != 0.
11 is a term because Sum_{k=0..10} exp(2*Pi*i*k^5/11) = 1 + 10*cos(2*Pi/11) != 0.
12 is not a term because Sum_{k=0..11} exp(2*Pi*i*k^5/12) = 0.
		

Crossrefs

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

Cf. A368959.