A147791 Primes p such that p^q-2 is prime for some prime q.

2, 3, 5, 7, 13, 19, 29, 31, 37, 43, 47, 61, 67, 71, 89, 103, 107, 109, 127, 131, 139, 151, 163, 173, 181, 191, 199, 211, 223, 229, 233, 239, 241, 257, 271, 277, 283, 293, 313, 337, 349, 359, 367, 379, 421, 433, 439, 443, 449, 457, 467, 491, 523, 541, 547, 569

Offset

1,1

Comments

For p>3, p^2-1 is divisible by 6. This follows from the fact that primes p>3 are of the form 6n+1 or 6n-1 and in either case p^2-1 is divisible by 6.

Links

Table of n, a(n) for n=1..56.

Example

2^2-2 = 2 is prime, so a(1)=2.
3^2-2 = 7 is prime, so a(2)=3.
For q=2,3,5, 199^q-2 is not prime. For q=7, 199^7-2 is prime, so a(27)=199.

Prog

(PARI) g2(n) = forprime(x=2, n, y=g(1000, x); if(y>0, print1(x", ")))
g(n, m) = p1=0; forprime(p=2, n, y=m^p-2; if(ispseudoprime(y), p1=p; break)); p1

Crossrefs

Sequence in context: A062252 A153800 A362777 * A169647 A072467 A062326

Adjacent sequences: A147788 A147789 A147790 * A147792 A147793 A147794

Keyword

nonn

Author

Cino Hilliard, Nov 13 2008

Extensions

Offset corrected by Mohammed Yaseen, Jul 20 2023

Status

approved