A268612 Primes p such that p + 2 k, for k = 1..7 are squarefree.

29, 83, 101, 191, 227, 389, 443, 479, 587, 641, 659, 677, 983, 1091, 1109, 1289, 1307, 1451, 1487, 2027, 2081, 2153, 2243, 2333, 2351, 2441, 2459, 2477, 2549, 2657, 2729, 2837, 2909, 2927, 2999, 3089, 3251, 3359, 3449, 3557, 3593, 4007

Offset: 1

Author

Zak Seidov, Feb 08 2016

Keywords

• nonn

Comments

Eight consecutive odd numbers starting with p are squarefree.

This is the longest set as p+16 in all cases is divisible by 9.

All terms are congruent to 11 mod 18.

Links

• Zak Seidov, Table of n, a(n) for n = 1..1592

Crossrefs

Cf. A049097, A049233.

Programs

Magma

[p: p in PrimesUpTo(4500) | forall{k: k in [1..7] | IsSquarefree(p+2*k)}]; // Vincenzo Librandi, Feb 09 2016

Mathematica

Select[Prime[Range[600]],AllTrue[#+2*Range[7],SquareFreeQ]&] (* Harvey P. Dale, Oct 19 2022 *)