login
Primes p such that p - 2 is squarefree.
5

%I #26 Aug 10 2024 22:33:56

%S 3,5,7,13,17,19,23,31,37,41,43,53,59,61,67,71,73,79,89,97,103,107,109,

%T 113,131,139,151,157,163,167,179,181,193,197,199,211,223,229,233,239,

%U 241,251,257,269,271,283,293,307,311,313,331,337,347,349,359,367,373

%N Primes p such that p - 2 is squarefree.

%C This sequence is infinite and its relative density in the sequence of the primes is equal to 2 * Product_{p prime} (1-1/(p*(p-1))) = 2 * A005596 = 0.747911... (Mirsky, 1949). - _Amiram Eldar_, Feb 27 2021

%H Seiichi Manyama, <a href="/A049231/b049231.txt">Table of n, a(n) for n = 1..10000</a>

%H Leon Mirsky, <a href="https://www.jstor.org/stable/2305811">The number of representations of an integer as the sum of a prime and a k-free integer</a>, The American Mathematical Monthly, Vol. 56, No. 1 (1949), pp. 17-19.

%F Primes p such that abs(mu(p-2)) = 1.

%t Select[Prime[Range[100]],SquareFreeQ[#-2]&] (* _Harvey P. Dale_, Mar 03 2018 *)

%o (PARI) isok(p) = isprime(p) && issquarefree(p-2); \\ _Michel Marcus_, Dec 31 2013

%Y Cf. A005117, A005596, A039787, A049233.

%K nonn

%O 1,1

%A _Labos Elemer_

%E Definition corrected by _Michel Marcus_, Dec 31 2013