A364453 - OEIS

%I #31 Aug 24 2024 15:43:22

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

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

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

%C a(7) > 5487.

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

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

%t lst={};Do[Do[p=5^(5^n)-k;If[PrimeQ[p],AppendTo[lst,k];Break[]],{k,2,11!}],{n,7}];lst

%t Table[k=1;Monitor[Parallelize[While[True,If[PrimeQ[5^(5^n)-k],Break[]];k++];k],k],{n,1,7}]

%t y[n_] := Module[{x = 5^(5^n)}, x - NextPrime[x, -1]]; Array[y, 7]

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

%Y Cf. A064722, A137841.

%Y Cf. A058220, A140331, A364452, A364454.

%K more,nonn

%O 0,1

%A _J.W.L. (Jan) Eerland_, Jul 25 2023

%E a(0) prepended and a(7) from _Michael S. Branicky_, Aug 24 2024