A137841 -id:A137841 - cp's OEIS frontend

A137840 Number of distinct n-ary operators in a quaternary logic.

4, 256, 4294967296, 340282366920938463463374607431768211456, 13407807929942597099574024998205846127479365820592393377723561443721764030073546976801874298166903427690031858186486050853753882811946569946433649006084096

Offset: 0

Ross Drewe, Feb 13 2008

The total number of n-ary operators in a k-valued logic is T = k^(k^n), i.e. if S is a set of k elements, there are T ways of mapping an ordered subset of n elements taken from S to an element of S. Some operators are "degenerate": the operator has arity p, if only p of the n input values influence the output. Therefore the set of operators can be partitioned into n+1 disjoint subsets representing arities from 0 to n.

Cf. A001146 (in binary logic), A055777 (in a ternary logic), A137841 (in a quinternary logic).

Subsequence of A000302.

a(n) = 4^(4^n).

A364453 Smallest k such that 5^(5^n) - k is prime.

Original entry on oeis.org

2, 4, 64, 124, 228, 10978, 73738, 66346

Offset: 0

J.W.L. (Jan) Eerland, Jul 25 2023

This is to 5 as A058220 is to 2 and A140331 is to 3.

a(7) > 5487.

			a(2) = 64 because 5^(5^2) - 64 = 298023223876953061 is prime.

Cf. A064722, A137841.

Cf. A058220, A140331, A364452, A364454.

lst={};Do[Do[p=5^(5^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[5^(5^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 5^(5^n)}, x - NextPrime[x, -1]]; Array[y, 7]

a(n) = my(x = 5^(5^n)); x - precprime(x);

a(n) = A064722(A137841(n)).

a(0) prepended and a(7) from Michael S. Branicky, Aug 24 2024

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A137840 Number of distinct n-ary operators in a quaternary logic.

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A364453 Smallest k such that 5^(5^n) - k is prime.

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