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

1,1

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

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 *)

Prog

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

Crossrefs

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

Sequence in context: A090126 A291566 A326580 * A241190 A276933 A110175

Adjacent sequences: A070192 A070193 A070194 * A070196 A070197 A070198

Keyword

easy,nonn

Author

Benoit Cloitre and Labos Elemer, May 06 2002

Status

approved