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 A293229 #22 Mar 04 2025 15:21:33
%S A293229 0,0,1,1,1,1,1,1,1,1,1,2,3,3,3,2,2,2,1,1,2,2,2,2,1,1,1,1,1,2,3,4,4,3,
%T A293229 3,3,2,2,3,3,3,3,3,2,2,2,2,3,3,3,3,2,2,2,2,2,3,3,3,3,2,3,3,3,3,4,4,4,
%U A293229 3,2,2,2,3,3,4,4,4,4,3,3,3,4,4,5,5,4,4,3,3,3,3,3,4,3,3,3,2,2,2,2,2,3,3,3,3,2
%N A293229 a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n+3) - A008966(4n+1)).
%C A293229 The sequence indicates about a possible bias (or lack of it) in the distribution of squarefree numbers among the numbers of the form 4k+1 vs. the numbers of the form 4k+3. See A293429 for another version.
%C A293229 The first negative term is a(1702) = -1.
%H A293229 Antti Karttunen, <a href="/A293229/b293229.txt">Table of n, a(n) for n = 0..10000</a>
%H A293229 Hans Havermann, <a href="/A293229/a293229.png">Plot of n, a(n) for n = 0..200000</a>
%H A293229 Hans Havermann, <a href="/A293229/a293229_1.png">Plot of n, a(n) for n = 0..10^7</a>
%F A293229 a(0) = 0; and for n > 0, a(n) = a(n-1) + (A008966(4n+3) - A008966(4n+1)).
%o A293229 (PARI) up_to = 10000; bias = 0; for(k=0,up_to,bias += (issquarefree((4*k)+3)-issquarefree((4*k)+1)); write("b293229.txt", k, " ", bias));
%o A293229 (Scheme)
%o A293229 ;; With memoization-macro definec.
%o A293229 (definec (A293229 n) (if (zero? n) n (+ (- (A008966 (+ 3 (* 4 n))) (A008966 (+ 1 (* 4 n)))) (A293229 (- n 1)))))
%Y A293229 Cf. A008966, A293428, A293429 (a variant).
%K A293229 sign
%O A293229 0,12
%A A293229 _Antti Karttunen_, Oct 12 2017