A267944 Primes that are a prime power minus two.

2, 3, 5, 7, 11, 17, 23, 29, 41, 47, 59, 71, 79, 101, 107, 137, 149, 167, 179, 191, 197, 227, 239, 241, 269, 281, 311, 347, 359, 419, 431, 461, 521, 569, 599, 617, 641, 659, 727, 809, 821, 827, 839, 857, 881

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

Cf. A000961, A049002, A246655, A267945.

Sequence in context: A175953 A362017 A040089 * A113161 A038953 A237288

Adjacent sequences: A267941 A267942 A267943 * A267945 A267946 A267947

Keyword

nonn

Author

Robert C. Lyons, Jan 22 2016

Status

approved