A268614 - OEIS

%I #16 Sep 08 2022 08:46:15

%S 5,13,29,37,41,101,109,113,137,157,181,193,229,257,281,317,353,389,

%T 397,401,409,433,461,509,541,569,613,617,641,653,661,677,757,761,769,

%U 797,821,829,857,877,937,941,977,1009,1021,1093,1109,1117,1129,1153,1193

%N Primes p such that p + 1 and p + 2 are squarefree.

%C All terms are == 1 mod 4, hence in all cases p+3 is divisible by 4 (and is not squarefree).

%H Amiram Eldar, <a href="/A268614/b268614.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Prime[Range[1000]], SquareFreeQ[# + 1] && SquareFreeQ[# + 2] &]

%o (Magma) [p: p in PrimesUpTo(1500) | IsSquarefree(p+1) and IsSquarefree(p+2)]; // _Vincenzo Librandi_, Feb 09 2016

%o (PARI) isok(p) = isprime(p) && issquarefree(p+1) && issquarefree(p+2); \\ _Michel Marcus_, Apr 01 2021

%Y Intersection of A049097 and A049233.

%Y Cf. A002144, A005117.

%K nonn

%O 1,1

%A _Zak Seidov_, Feb 08 2016