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

1,1

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

Mathematica

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

Prog

(Magma) [p: p in PrimesUpTo(1500) | IsSquarefree(p+1) and IsSquarefree(p+2)]; // Vincenzo Librandi, Feb 09 2016
(PARI) isok(p) = isprime(p) && issquarefree(p+1) && issquarefree(p+2); \\ Michel Marcus, Apr 01 2021

Crossrefs

Intersection of A049097 and A049233.

Cf. A002144, A005117.

Sequence in context: A133204 A207040 A309588 * A152658 A347836 A100877

Adjacent sequences: A268611 A268612 A268613 * A268615 A268616 A268617

Keyword

nonn

Author

Zak Seidov, Feb 08 2016

Status

approved