A049231 Primes p such that p - 2 is squarefree.

3, 5, 7, 13, 17, 19, 23, 31, 37, 41, 43, 53, 59, 61, 67, 71, 73, 79, 89, 97, 103, 107, 109, 113, 131, 139, 151, 157, 163, 167, 179, 181, 193, 197, 199, 211, 223, 229, 233, 239, 241, 251, 257, 269, 271, 283, 293, 307, 311, 313, 331, 337, 347, 349, 359, 367, 373

Offset: 1

Author

Labos Elemer

Keywords

• nonn

Comments

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

Links

• Seiichi Manyama, Table of n, a(n) for n = 1..10000
• 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.

Crossrefs

Cf. A005117, A005596, A039787, A049233.

Programs

Mathematica

Select[Prime[Range[100]],SquareFreeQ[#-2]&] (* Harvey P. Dale, Mar 03 2018 *)

PARI

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

Formula

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

Extensions

Definition corrected by Michel Marcus, Dec 31 2013