A268614 Primes p such that p + 1 and p + 2 are squarefree.

5, 13, 29, 37, 41, 101, 109, 113, 137, 157, 181, 193, 229, 257, 281, 317, 353, 389, 397, 401, 409, 433, 461, 509, 541, 569, 613, 617, 641, 653, 661, 677, 757, 761, 769, 797, 821, 829, 857, 877, 937, 941, 977, 1009, 1021, 1093, 1109, 1117, 1129, 1153, 1193

Offset: 1

Author

Zak Seidov, Feb 08 2016

Keywords

• nonn

Comments

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Intersection of A049097 and A049233.

Cf. A002144, A005117.

Programs

Magma

[p: p in PrimesUpTo(1500) | IsSquarefree(p+1) and IsSquarefree(p+2)]; // Vincenzo Librandi, Feb 09 2016

Mathematica

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

PARI

isok(p) = isprime(p) && issquarefree(p+1) && issquarefree(p+2); \\ Michel Marcus, Apr 01 2021