cp's OEIS Frontend

A068361 Numbers n such that the number of squarefree numbers between prime(n) and prime(n+1) = prime(n+1)-prime(n)-1.

%I A068361 #19 Dec 13 2024 18:21:54
%S A068361 1,3,10,13,26,33,60,89,104,113,116,142,148,201,209,212,234,265,268,
%T A068361 288,313,320,332,343,353,384,398,408,477,484,498,542,545,551,577,581,
%U A068361 601,625,636,671,719,723,726,745,794,805,815,862,864,884,944,964,995,1054
%N A068361 Numbers n such that the number of squarefree numbers between prime(n) and prime(n+1) = prime(n+1)-prime(n)-1.
%C A068361 Also numbers k such that all numbers from prime(k) to prime(k+1) are squarefree. All such primes are twins, so this is a subset of A029707. The other twin primes are A061368. - _Gus Wiseman_, Dec 11 2024
%H A068361 Amiram Eldar, <a href="/A068361/b068361.txt">Table of n, a(n) for n = 1..10000</a>
%F A068361 n such that A061398(n) = prime(n+1)-prime(n)-1.
%F A068361 prime(a(n)) = A061351(n). - _Gus Wiseman_, Dec 11 2024
%t A068361 Select[Range[100],And@@SquareFreeQ/@Range[Prime[#],Prime[#+1]]&] (* _Gus Wiseman_, Dec 11 2024 *)
%o A068361 (PARI) isok(n) = for (k=prime(n)+1, prime(n+1)-1, if (!issquarefree(k), return (0))); 1; \\ _Michel Marcus_, Apr 29 2016
%Y A068361 A subset of A029707 (lesser index of twin primes).
%Y A068361 Prime index of each (prime) term of A061351.
%Y A068361 Positions of zeros in A061399.
%Y A068361 For perfect power instead of squarefree we have A377436, zeros of A377432.
%Y A068361 Positions of zeros in A377784.
%Y A068361 The rest of the twin primes are at A378620, indices of A061368.
%Y A068361 A000040 lists the primes, differences A001223, (run-lengths A333254, A373821).
%Y A068361 A005117 lists the squarefree numbers, differences A076259.
%Y A068361 A006562 finds balanced primes.
%Y A068361 A013929 lists the nonsquarefree numbers, differences A078147.
%Y A068361 A014574 is the intersection of A006093 and A008864.
%Y A068361 A038664 locates the first prime gap of size 2n.
%Y A068361 A046933 counts composite numbers between primes.
%Y A068361 A061398 counts squarefree numbers between primes, zeros A068360.
%Y A068361 A120327 gives the least nonsquarefree number >= n.
%Y A068361 Cf. A000720, A007674, A013928, A057627, A070321, A071403, A072284, A073247, A112925, A122535, A155752, A224363, A240473, A251092.
%K A068361 nonn
%O A068361 1,2
%A A068361 _Benoit Cloitre_, Feb 28 2002