A061351 - OEIS

%I #8 Aug 09 2015 14:37:59

%S 2,5,29,41,101,137,281,461,569,617,641,821,857,1229,1289,1301,1481,

%T 1697,1721,1877,2081,2129,2237,2309,2381,2657,2729,2801,3389,3461,

%U 3557,3917,3929,4001,4217,4241,4421,4637,4721,5009,5441,5477,5501,5657,6089

%N Between p and the next prime either there are no numbers or there is a single squarefree number.

%C Apart from the initial 2, the lesser of twin primes {p, p+2} such that the middle term p+1 is squarefree: intersection[{A014574(n)},{A005117(n)}].

%H Harry J. Smith, <a href="/A061351/b061351.txt">Table of n, a(n) for n=0,...,1000</a>

%e Between 29 and 31 the only composite is 30, a squarefree number. If next(p)-p>2, a nonsquarefree integer always arises between them.

%o (PARI) { n=0; p=3; f="b061351.txt"; write(f, "0 2"); forprime (q=5, 355723, if (q-p == 2, if (issquarefree(p+1), write(f, n++, " ", p))); p=q ) } \\ _Harry J. Smith_, Jul 21 2009

%Y Cf. A005117, A013929, A000040, A001359, A014574, A061398, A061399.

%K nonn

%O 0,1

%A _Labos Elemer_, Jun 07 2001