A350418 a(n) is the number of universal binary n-state logic gates.

1, 2, 3774, 942897552, 76897278357005640

Offset: 1

Author

Woosuk Kwak, Dec 29 2021

Keywords

• nonn
• hard
• more

Comments

The number of closed binary operations F on a set of order n such that {F} is functionally complete.

a(3) computed by Craig Gidney, corrected by Code Golf Stack Exchange user AnttiP.

a(4) computed by Code Golf Stack Exchange user AnttiP.

a(5) computed by Code Golf Stack Exchange user gsitcia.

Examples

			For n = 2, the two universal logic gates are NAND and NOR.
		

Links

• R. O. Davies, On n-Valued Sheffer Functions, Mathematical Logic Quarterly, 25 (1979), 293-298.
• Craig Gidney, Exploring Universal Ternary Gates.
• Woosuk Kwak, Counting universal n-ary logic gates, Code Golf Stack Exchange.
• Wikipedia, Logic gate.
• Wikipedia, Functional completeness.

Crossrefs

A002489(n) counts all binary n-state logic gates.

Formula

Limit_{n->oo} a(n)/A002489(n) = 1/e.

Extensions

a(5) added by Woosuk Kwak, Nov 23 2023