A364452 Smallest k such that 4^(4^n) - k is prime.

1, 5, 5, 159, 569, 1557, 2439, 25353, 24317, 164073

Offset: 0

Author

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

Keywords

• nonn
• more

Comments

This is to 4 as A058220 is to 2 and A140331 is to 3.

a(8) > 22174.

Examples

			a(2) = 5 because 4^(4^2) - 5 = 4294967291 is prime.
		

Crossrefs

Cf. A064722, A137840.

Cf. A058220, A140331, A364453, A364454.

Programs

Mathematica

lst={};Do[Do[p=4^(4^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[4^(4^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 4^(4^n)}, x - NextPrime[x, -1]]; Array[y, 7]

PARI

a(n) = my(x = 4^(4^n)); x - precprime(x);

Formula

a(n) = A064722(A137840(n)).

a(n) = A058220(2*n+1). - Michael S. Branicky, Aug 23 2024

Extensions

a(8) using search and a(9) using A058220 from Michael S. Branicky, Aug 23 2024

a(0) = 1 prepended by Michael S. Branicky, Apr 20 2025