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

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

Offset: 0

Author

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

Keywords

• more
• nonn

Comments

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

a(7) > 5487.

Examples

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

Crossrefs

Cf. A064722, A137841.

Cf. A058220, A140331, A364452, A364454.

Programs

Mathematica

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]

PARI

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

Formula

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

Extensions

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