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} (1-1/(p*(p-1))) = 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 k-free integer, The American Mathematical Monthly, Vol. 56, No. 1 (1949), pp. 17-19.
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]&] (* Jean-François Alcover, Nov 22 2015 *)
PROG
(PARI) isok(p) = isprime(p) && issquarefree(p+2); \\ Michel Marcus, Dec 31 2013
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Definition simplified by Michel Marcus, Dec 31 2013
STATUS
approved