

A340154


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


1



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
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OFFSET

1,1


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).


LINKS



EXAMPLE

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


MATHEMATICA

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


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



