A364454 Smallest k such that 6^(6^n) - k is prime.

1, 7, 35, 587, 629, 1819, 106843

Offset: 0

Author

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

Keywords

• more
• nonn

Comments

This is to 6 as A058220 is to 2 and A140331 is to 3.

Examples

			a(2) = 35 because 6^(6^2) - 35 = 10314424798490535546171949021 is prime.
		

Crossrefs

Cf. A058220, A140331, A364452, A364453.

Programs

Mathematica

lst={};Do[Do[p=6^(6^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst
Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[6^(6^n)-k],Break[]];k++];k],k],{n,1,7}]
y[n_] := Module[{x = 6^(6^n)}, x - NextPrime[x, -1]]; Array[y, 7]

PARI

a(n) = my(x = 6^(6^n)); x - precprime(x);

Extensions

a(6) from Michael S. Branicky, Aug 23 2024

a(0)=1 prepended by Alois P. Heinz, Aug 23 2024