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 A086742 #16 Oct 08 2022 00:02:03 %S A086742 1,1,1,2,1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20, %T A086742 1,2,3,4,5,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22, %U A086742 23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47 %N A086742 Start with a(0)=1, then k-th run is 1,2,3,..., a(0) + a(1) + a(2) + ... + a(k-1). %F A086742 a(0) + a(1) + a(2) + ... + a(r(k)) = A006893(k) where r(k) denotes the index of the end of the k-th run. I.e., the first 4 runs are (1), (1), (1, 2), (1, 2, 3, 4, 5), so the 4th run ends with 5=a(8), so r(4)=8 and a(0) + a(1) + a(2) + ... + a(r(4)) = 1+1+1+2+1+2+3+4+5 = 20 which is A006893(4). %e A086742 The first 3 runs are (1), (1), (1, 2) and a(0) + a(1) + a(2) + a(3) = 1+1+1+2 = 5, so the 4th run is 1, 2, 3, 4, 5 and the sequence continues: (1), (1), (1, 2), (1, 2, 3, 4, 5), ... %Y A086742 Cf. A006893. %K A086742 nonn %O A086742 0,4 %A A086742 _Benoit Cloitre_, Jul 29 2003