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 A309898 #15 Aug 29 2019 15:47:25 %S A309898 1,1,2,1,1,3,2,1,1,4,2,1,3,1,5,2,1,1,2,3,6,4,1,1,2,1,1,7,3,2,1,5,1,4, %T A309898 2,8,1,3,1,2,1,1,2,6,9,3,4,1,1,5,2,1,1,3,10,2,1,1,7,4,2,1,3,1,2,11,1, %U A309898 5,6,1,2,3,4,1,8,1,2,12,1,1,3,2,1,1,4,5,2,1,3,7,13 %N A309898 For each b = 1, 2, 3, ... numbers k = 1, 2, 3, ... are inserted into the blanks within the sequence along with k * b blanks, skipping existing terms in the sequence. %C A309898 b = 1 for all blanks forms A003602. b = k yields A002260. %H A309898 Seiichi Manyama, <a href="/A309898/b309898.txt">Table of n, a(n) for n = 1..10000</a> %e A309898 The first 21 terms are constructed as follows: %e A309898 1 _ 2 _ _ 3 _ _ _ 4 _ _ _ _ 5 _ _ _ _ _ . %e A309898 1 _ _ 2 _ _ _ _ 3 _ _ _ _ _ _ . %e A309898 1 _ _ _ 2 _ _ _ _ _ _ 3 . %e A309898 1 _ _ _ _ 2 _ _ _ . %e A309898 1 _ _ _ _ _ 2 . %e A309898 1 _ _ _ _ . %e A309898 1 _ _ _ . %e A309898 1 _ _ . %e A309898 1 _ . %e A309898 1 . %e A309898 1 1 2 1 1 3 2 1 1 4 2 1 3 1 5 2 1 1 2 3 . %o A309898 (Python) %o A309898 seq = [] %o A309898 b = 2 %o A309898 for n in range(1, 100): %o A309898 seq += [n] + [-1] * n %o A309898 while -1 in seq: %o A309898 i = seq.index(-1) %o A309898 seq[i] = 1 %o A309898 k = 2 %o A309898 blanks = b %o A309898 for s in range(i + 1, len(seq)): %o A309898 if seq[s] == -1: %o A309898 blanks -= 1 %o A309898 if blanks < 0: %o A309898 seq[s] = k %o A309898 blanks = k * b %o A309898 k += 1 %o A309898 b += 1 %o A309898 print(seq) %Y A309898 Cf. A309898, A003602, A002260, A306470. %K A309898 nonn,easy %O A309898 1,3 %A A309898 _Jan Koornstra_, Aug 21 2019