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A131433 Number of prime knots on n crossings having Arf invariant 0. 1

%I #18 Feb 07 2023 15:14:37

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

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

%H KnotInfo, <a href="https://knotinfo.math.indiana.edu/">Table of Knots</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ArfInvariant.html">Arf Invariant</a>

%F a(n) = A002863(n) - A131434(n). - _Andrew Howroyd_, Jan 15 2023

%e 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

%Y Cf. A002863, A131434.

%K nonn,more

%O 1,7

%A _Eric W. Weisstein_, Jul 10 2007

%E a(11)-a(12) added using data from the KnotInfo database (see Links above) by _Emma Joe Anderson_, Jan 15 2023

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Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)