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%I #25 Jun 03 2020 12:12:17
%S 2,3,5,7,11,17,23,29,41,47,59,71,79,101,107,137,149,167,179,191,197,
%T 227,239,241,269,281,311,347,359,419,431,461,521,569,599,617,641,659,
%U 727,809,821,827,839,857,881
%N Primes that are a prime power minus two.
%C The sequence is probably infinite, since it includes all the terms of A001359 (Lesser of twin primes).
%C 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
%H Robert Israel, <a href="/A267944/b267944.txt">Table of n, a(n) for n = 1..10000</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bunyakovsky_conjecture#Generalized_Bunyakovsky_conjecture">Generalized Bunyakovsky conjecture</a>
%e 2 is in the sequence because 2 = 2^2 - 2.
%e 3 is in the sequence because 3 = 5^1 - 2.
%e 5 is in the sequence because 5 = 7^1 - 2.
%e 7 is in the sequence because 7 = 3^2 - 2.
%p select(t -> isprime(t) and nops(numtheory:-factorset(t+2))=1, [2, seq(i,i=3..1000, 2)]); # _Robert Israel_, Jan 22 2016
%t A267944Q = PrimeQ@# && Length@FactorInteger[# + 2] == 1 & (* _JungHwan Min_, Jan 24 2016 *)
%t Select[Array[Prime, 100], Length@FactorInteger[# + 2] == 1 &] (* _JungHwan Min_, Jan 24 2016 *)
%t Select[Prime[Range[300]],PrimePowerQ[#+2]&] (* _Harvey P. Dale_, Nov 28 2016 *)
%o (Sage) [n - 2 for n in prime_powers(1, 1000) if is_prime(n - 2)]
%o (PARI) lista(nn) = {forprime(p=2, nn, if (isprimepower(p+2), print1(p, ", ")););} \\ _Michel Marcus_, Jan 22 2016
%Y Cf. A000961, A049002, A246655, A267945.
%K nonn
%O 1,1
%A _Robert C. Lyons_, Jan 22 2016
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