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A162712
Primes p such that 3^p - 2^p - 2 is also prime.
1
2, 3, 43, 61, 5563, 10093
OFFSET
1,1
COMMENTS
The associated 3^p-2^p-2 are in A162713.
The list of k such that 3^k-2^k-2 is prime is: 2, 3, 43, 61, 63, 1369, ..., where 63 and 1369 are not prime.
No other term <= 15000. - Emeric Deutsch, Aug 03 2009
a(7) > 25000. - Tyler NeSmith, Jul 10 2021
a(7) > 2*10^5. - Michael S. Branicky, Sep 11 2024
EXAMPLE
2 is in the sequence because 3^2-2^2-2 = 3 is prime.
3 is in the sequence because 3^3-2^3-2 = 17 is prime.
MAPLE
a := proc(n) if isprime(n) and isprime(3^n-2^n-2) then n end if end proc:
seq(a(n), n = 1 .. 15000); # Emeric Deutsch, Aug 03 2009
MATHEMATICA
Select[Prime[Range[11000]], PrimeQ[3^# - 2^# - 2] &] (* Vincenzo Librandi, Sep 25 2015 *)
PROG
(PARI) forprime(p=2, 1e3, if (isprime(3^p-2^p-2), print1(p, ", "))) \\ Altug Alkan, Sep 25 2015
(Magma) [p: p in PrimesUpTo(1000) | IsPrime(3^p-2^p-2)]; // Vincenzo Librandi, Sep 26 2015
CROSSREFS
Cf. A162713.
Sequence in context: A255092 A237414 A051099 * A182217 A233314 A062581
KEYWORD
nonn,more
AUTHOR
Vincenzo Librandi, Jul 11 2009
EXTENSIONS
Edited by R. J. Mathar, Jul 26 2009
a(5)-a(6) from Emeric Deutsch, Aug 03 2009
STATUS
approved