A340154 Primes p such that p == 5 (mod 6) and p+1 is squarefree.

5, 29, 41, 101, 113, 137, 173, 257, 281, 317, 353, 389, 401, 461, 509, 569, 617, 641, 653, 677, 761, 797, 821, 857, 929, 941, 977, 1109, 1181, 1193, 1217, 1229, 1289, 1301, 1361, 1373, 1409, 1433, 1481, 1553, 1613, 1697, 1721, 1877, 1901, 1913, 1973, 2081, 2129

Offset: 1

Author

Amiram Eldar, Dec 29 2020

Keywords

• nonn
• easy

Comments

Clary and Fabrykowski (2004) proved that this sequence is infinite, and that its relative density in the sequence of primes of the form 6*k+5 (A007528) is 4*A/5 = 0.29916465..., where A is Artin's constant (A005596).

Examples

			5 is a term since it is prime, 5 == 5 (mod 6), and 5+1 = 6 = 2*3 is squarefree.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Stuart Clary and Jacek Fabrykowski, Arithmetic progressions, prime numbers, and squarefree integers, Czechoslovak Mathematical Journal, Vol. 54, No. 4 (2004), pp. 915-927.

Crossrefs

Intersection of A007528 and A049097.

Cf. A005117, A005596.

Programs

Mathematica

Select[Range[2000], Mod[#, 6] == 5 && PrimeQ[#] && SquareFreeQ[# + 1] &]