A356330 a(n) is the least prime p such that p^n-2 is prime.

5, 2, 19, 3, 3, 3, 7, 7, 3, 53, 1171, 7, 19, 5, 7, 73, 31, 61, 19, 19, 31, 3, 19, 17, 349, 5, 499, 7, 1021, 17, 7, 491, 823, 463, 1171, 59, 3, 19, 199, 179, 3, 29, 1609, 463, 373, 379, 2539, 439, 349, 5, 1051, 241, 439, 467, 61, 89, 433, 563, 139, 499, 139, 607, 409, 1607, 433, 1423, 2719, 7933, 31

Offset

1,1

Comments

a(n) = 3 for n > 2 in A014224.

Links

Robert Israel, Table of n, a(n) for n = 1..1000

Example

a(3) = 19 because 19 and 19^3 - 2 = 6857 are prime and no prime < 19 works.

Maple

f:= proc(n) local p;
p:= 1;
do
  p:= nextprime(p);
  if isprime(p^n-2) then return p fi
od
end proc:
map(f, [$1..100]);

Mathematica

a[n_] := Module[{p = 2}, While[!PrimeQ[p^n - 2], p = NextPrime[p]]; p]; Array[a, 100] (* Amiram Eldar, Aug 04 2022 *)

Prog

(Python)
from sympy import isprime, nextprime
def a(n):
    p = 2
    while not isprime(p**n - 2): p = nextprime(p)
    return p
print([a(n) for n in range(1, 70)]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A014224.

Sequence in context: A286154 A367288 A304635 * A306198 A327316 A206582

Adjacent sequences: A356327 A356328 A356329 * A356331 A356332 A356333

Keyword

nonn

Author

Robert Israel, Aug 03 2022

Status

approved