%I A061351
%S A061351 2,5,29,41,101,137,281,461,569,617,641,821,857,1229,1289,1301,1481,
%T A061351 1697,1721,1877,2081,2129,2237,2309,2381,2657,2729,2801,3389,3461,3557,
%U A061351 3917,3929,4001,4217,4241,4421,4637,4721,5009,5441,5477,5501,5657,6089
%N A061351 Between p and the next prime either there are no numbers or there is 
               a single square-free number.
%C A061351 Apart from the initial 2, the lesser of twin primes {p, p+2} such that 
               the middle term p+1 is square-free: intersection[{A014574(n)},{A005117(n)}]
%H A061351 Harry J. Smith, <a href="b061351.txt">Table of n, a(n) for n=0,...,1000</
               a>
%e A061351 Between 29 and 31 the only composite is 30, a square-free number. If 
               next(p)-p>2, a non-square-free integer always arises between them.
%o A061351 (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 
               ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 21 2009]
%Y A061351 Cf. A005117, A013929, A000040, A001359, A014574, A061398, A061399.
%Y A061351 Sequence in context: A134449 A103579 A161500 this_sequence A126107 A083472 
               A057794
%Y A061351 Adjacent sequences: A061348 A061349 A061350 this_sequence A061352 A061353 
               A061354
%K A061351 nonn
%O A061351 0,1
%A A061351 Labos E. (labos(AT)ana.sote.hu), Jun 07 2001