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

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

Offset

1,1

Comments

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

a(8) > 22174.

Links

Table of n, a(n) for n=1..9.

Formula

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

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

Example

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

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]

Prog

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

Crossrefs

Cf. A064722, A137840.

Cf. A058220, A140331, A364453, A364454.

Sequence in context: A229767 A369753 A215729 * A094463 A055928 A213145

Adjacent sequences: A364449 A364450 A364451 * A364453 A364454 A364455

Keyword

more,nonn

Author

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

Extensions

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

Status

approved