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 A232740 #12 Dec 12 2013 03:24:23
%S A232740 1,2,1,2,1,2,1,1,2,1,1,2,1,1,2,1,1,1,2,1,1,1,2,1,1,1,1,2,1,1,1,1,2,1,
%T A232740 1,1,1,2,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,2,1,1,1,1,1,1,2,1,1,1,1,1,1,
%U A232740 2,1,1,1,1,1,1,2,1,1,1,1,1,1,1,2,1,1,1
%N A232740 a(n) = Number of terms of A232739 which occur between each consecutive terms of A005228, in range A005228(n)..A005228(n+1).
%C A232740 Do any other values appear than 1 and 2? The 2's seem to be getting rarer, as zeros correspondingly get rarer in A232750. This has some implications about how the ratio A005228(n)/A232739(n) will develop. Please see also the comments and graph-drawing link in A232739.
%H A232740 Antti Karttunen, <a href="/A232740/b232740.txt">Table of n, a(n) for n = 1..2009</a>
%H A232740 <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>
%F A232740 a(n) = A232753(A005228(n+1)) - A232753(A005228(n)).
%e A232740 The two sequences begin as:
%e A232740 A005228: 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, ...
%e A232740 A232739: 2, 4,6, 9, 13,17, 22, 28,34, 41, 49, 58,67, 77, ...
%e A232740 Grouping together the terms of A232739 that occur between two successive terms of A232739, we get {2}, {4,6}, {9}, {13,17}, {22}, {28,34}, {41}, {49}, {58,67}, {77}, ... and counting how many terms are in each such group, we get 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, ..., the first terms of this sequence.
%o A232740 (Scheme)
%o A232740 (define (A232740 n) (- (A232753 (A005228 (+ n 1))) (A232753 (A005228 n))))
%Y A232740 Cf. A005228, A232739, A232750, A232753.
%K A232740 nonn
%O A232740 1,2
%A A232740 _Antti Karttunen_, Dec 04 2013