

A049233


Primes p such that p + 2 is squarefree.


6



3, 5, 11, 13, 17, 19, 29, 31, 37, 41, 53, 59, 67, 71, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 157, 163, 179, 181, 191, 193, 197, 199, 211, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 317, 337, 347, 353, 379, 383, 389
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OFFSET

1,1


COMMENTS

A001359 (lesser of twin primes) is a subsequence.  Michel Marcus, Aug 10 2018
This sequence is infinite and its relative density in the sequence of primes is equal to 2 * Product_{p prime} (11/(p*(p1)) = 2 * A005596 = 0.747911... (Mirsky, 1949).  Amiram Eldar, Dec 29 2020


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000
Denis Xavier Charles, Sieve Methods, Master's Thesis, 2000, p. 93.
Leon Mirsky, The number of representations of an integer as the sum of a prime and a kfree integer, The American Mathematical Monthly, Vol. 56, No. 1 (1949), pp. 1719.


MAPLE

A049233:=n>`if`(isprime(n) and numtheory[issqrfree](n+2), n, NULL): seq(A049233(n), n=1..600); # Wesley Ivan Hurt, Nov 22 2015


MATHEMATICA

Select[Prime[Range[100]], SquareFreeQ[#+2]&] (* JeanFrançois Alcover, Nov 22 2015 *)


PROG

(PARI) isok(p) = isprime(p) && issquarefree(p+2); \\ Michel Marcus, Dec 31 2013


CROSSREFS

Cf. A001359, A005117, A005596.
Sequence in context: A338018 A059352 A059309 * A045402 A059634 A059315
Adjacent sequences: A049230 A049231 A049232 * A049234 A049235 A049236


KEYWORD

nonn


AUTHOR

Labos Elemer


EXTENSIONS

Definition simplified by Michel Marcus, Dec 31 2013


STATUS

approved



