OFFSET
1,1
COMMENTS
The sequence is probably infinite, since it includes all the terms of A001359 (Lesser of twin primes).
Also includes A049002. The generalized Bunyakovsky conjecture implies that for every k there are infinitely many terms of the form p^k - 2. - Robert Israel, Jan 22 2016
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Generalized Bunyakovsky conjecture
EXAMPLE
2 is in the sequence because 2 = 2^2 - 2.
3 is in the sequence because 3 = 5^1 - 2.
5 is in the sequence because 5 = 7^1 - 2.
7 is in the sequence because 7 = 3^2 - 2.
MAPLE
select(t -> isprime(t) and nops(numtheory:-factorset(t+2))=1, [2, seq(i, i=3..1000, 2)]); # Robert Israel, Jan 22 2016
MATHEMATICA
A267944Q = PrimeQ@# && Length@FactorInteger[# + 2] == 1 & (* JungHwan Min, Jan 24 2016 *)
Select[Array[Prime, 100], Length@FactorInteger[# + 2] == 1 &] (* JungHwan Min, Jan 24 2016 *)
Select[Prime[Range[300]], PrimePowerQ[#+2]&] (* Harvey P. Dale, Nov 28 2016 *)
PROG
(Sage) [n - 2 for n in prime_powers(1, 1000) if is_prime(n - 2)]
(PARI) lista(nn) = {forprime(p=2, nn, if (isprimepower(p+2), print1(p, ", ")); ); } \\ Michel Marcus, Jan 22 2016
CROSSREFS
KEYWORD
nonn
AUTHOR
Robert C. Lyons, Jan 22 2016
STATUS
approved