cp's OEIS Frontend

A375927 Numbers k such that A005117(k+1) - A005117(k) = 1. In other words, the k-th squarefree number is 1 less than the next.

%I A375927 #13 Sep 15 2024 14:40:57
%S A375927 1,2,4,5,7,9,10,14,15,18,19,21,22,24,25,27,28,30,35,36,38,40,41,43,44,
%T A375927 46,48,49,51,53,54,58,59,62,63,65,66,68,69,71,72,74,76,79,80,82,84,85,
%U A375927 87,88,90,94,96,97,101,102,105,107,108,110,111,113,114,116
%N A375927 Numbers k such that A005117(k+1) - A005117(k) = 1. In other words, the k-th squarefree number is 1 less than the next.
%C A375927 The asymptotic density of this sequence is Product_{p prime} (1 - 1/(p^2-1)) = 0.53071182... (A065469). - _Amiram Eldar_, Sep 15 2024
%H A375927 Amiram Eldar, <a href="/A375927/b375927.txt">Table of n, a(n) for n = 1..10000</a>
%e A375927 The squarefree numbers are 1, 2, 3, 5, 6, 7, 10, 11, 13, 14, 15, 17, 19, 21, 22, 23, 26, 29, 30, ... which first increase by one after terms 1, 2, 4, 5, ...
%t A375927 Join@@Position[Differences[Select[Range[100],SquareFreeQ[#]&]],1]
%o A375927 (PARI) lista(kmax) = {my(is1 = 1, is2, c = 1); for(k = 2, kmax, is2 = issquarefree(k); if(is2, c++); if(is1 && is2, print1(c-1, ", ")); is1 = is2);} \\ _Amiram Eldar_, Sep 15 2024
%Y A375927 Positions of 1's in A076259.
%Y A375927 For prime-powers (A246655) we have A375734.
%Y A375927 First differences are A373127.
%Y A375927 For nonsquarefree instead of squarefree we have A375709.
%Y A375927 For nonprime numbers we have A375926, differences A373403.
%Y A375927 For composite numbers we have A375929.
%Y A375927 The complement is A375930, differences A120992.
%Y A375927 A005117 lists the squarefree numbers, first differences A076259.
%Y A375927 A013929 lists the nonsquarefree numbers, first differences A078147.
%Y A375927 A053797 gives lengths of runs of nonsquarefree numbers, firsts A373199.
%Y A375927 A375707 counts squarefree numbers between consecutive nonsquarefree numbers.
%Y A375927 Cf. A007674, A061399, A065469, A072284, A110969, A294242, A373409, A373410, A373573.
%K A375927 nonn
%O A375927 1,2
%A A375927 _Gus Wiseman_, Sep 12 2024