This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A061351 #10 Jan 26 2025 12:48:41
%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,
%U A061351 3557,3917,3929,4001,4217,4241,4421,4637,4721,5009,5441,5477,5501,5657,6089
%N A061351 Between p and the next prime either there are no numbers or there is a single squarefree number.
%C A061351 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 A061351 Harry J. Smith, <a href="/A061351/b061351.txt">Table of n, a(n) for n=0,...,1000</a>
%e A061351 Between 29 and 31 the only composite is 30, a squarefree number. If next(p)-p>2, a nonsquarefree integer always arises between them.
%t A061351 Join[{2},Select[Partition[Prime[Range[800]],2,1],#[[2]]-#[[1]]==2&&SquareFreeQ[#[[1]]+1]&][[;;,1]]] (* _Harvey P. Dale_, Jan 26 2025 *)
%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 ) } \\ _Harry J. Smith_, Jul 21 2009
%Y A061351 Cf. A005117, A013929, A000040, A001359, A014574, A061398, A061399.
%K A061351 nonn
%O A061351 0,1
%A A061351 _Labos Elemer_, Jun 07 2001