A070195 Squarefree numbers sandwiched between a pair of twin primes.

6, 30, 42, 102, 138, 282, 462, 570, 618, 642, 822, 858, 1230, 1290, 1302, 1482, 1698, 1722, 1878, 2082, 2130, 2238, 2310, 2382, 2658, 2730, 2802, 3390, 3462, 3558, 3918, 3930, 4002, 4218, 4242, 4422, 4638, 4722, 5010, 5442, 5478, 5502, 5658, 6090, 6198

Offset: 1

Author

Benoit Cloitre and Labos Elemer, May 06 2002

Keywords

• easy
• nonn

Comments

Numbers k such that k is squarefree, k-1 and k+1 are primes.

Intersection of A005117 and A014574. - Michel Marcus, Mar 06 2014

Also, intersection of A077064 and A077067. - Zak Seidov, Mar 20 2016

All terms are multiples of 6. - Zak Seidov, Mar 20 2016

All terms == 6 (mod 12). - Robert Israel, Mar 21 2016

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A005117, A014574, A077064, A077067. - Zak Seidov, Mar 20 2016

Programs

Maple

select(t -> numtheory:-issqrfree(t) and isprime(t+1) and isprime(t-1),
[seq(i, i=6..10000, 12)]); # Robert Israel, Mar 21 2016

Mathematica

Select[12 * Range[0, 500] + 6, PrimeQ[#-1] && PrimeQ[#+1] && SquareFreeQ[#] &] (* Amiram Eldar, May 23 2022 *)

PARI

{forstep(n=6,8000,12,if(issquarefree(n)&&isprime(n-1)&&isprime(n+1),print1(n",")));} \\ Zak Seidov, Mar 20 2016