A131433 Number of prime knots on n crossings having Arf invariant 0.

0, 0, 0, 0, 1, 1, 3, 10, 25, 82, 283, 1106

Offset

1,7

Links

Table of n, a(n) for n=1..12.

KnotInfo, Table of Knots

Eric Weisstein's World of Mathematics, Arf Invariant

Formula

a(n) = A002863(n) - A131434(n). - Andrew Howroyd, Jan 15 2023

Example

For n <= 6, 5_2 and 6_1 are the only prime knots with Arf Invariant 0. (The unknot is not considered prime nor composite, much like the integer 1.) - Emma Joe Anderson, Jan 15 2023

Crossrefs

Cf. A002863, A131434.

Sequence in context: A026950 A095052 A196984 * A110713 A098702 A100001

Adjacent sequences: A131430 A131431 A131432 * A131434 A131435 A131436

Keyword

nonn,more

Author

Eric W. Weisstein, Jul 10 2007

Extensions

a(11)-a(12) added using data from the KnotInfo database (see Links above) by Emma Joe Anderson, Jan 15 2023

Status

approved