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 A077712 #18 Sep 16 2023 15:59:27 %S A077712 1,10,101,110,1001,1010,10001,10010,100001,100010,1000001,1000010, %T A077712 10000001,10000010,100000001,100000010,1000000001,1000000010, %U A077712 10000000001,10000000010,100000000010,1000000000001,10000000000001 %N A077712 a(1) = 1, a(n) = the smallest squarefree number > a(n-1) which contains all the digits of a(n-1). %C A077712 Conjecture: Terms contain only two types of digits, i.e., 0 and 1. %C A077712 Beginning with a(3), sequence follows a regular pattern: 10^2+1, 10^2+10, 10^3+1, 10^3+10, etc. until at a(21) the pattern is disrupted by 10^11+1, which is not squarefree (see A086982). 10^12+10 is also absent from the sequence since it is also not squarefree. The pattern resumes after this disruption until the next occurrence of 10^k+1 which is not squarefree, k=21, 33, 39, 55, ... The conjecture that the sequence is composed of terms containing only the digits 0 and 1 is certainly true up to 10^406+1 where both it and 10^407+1 are not squarefree. Indeed beginning with a(3) the terms contain exactly two 1 digits and the rest 0's up to this point. The term following 10^406+10 will introduce a third nonzero digit, perhaps a 1, but the pattern of the sequence changes dramatically at this point. - _Ray Chandler_, Aug 02 2003 %C A077712 Term following a(739)=10^406+10 is a(740)=10^407+11 so the conjecture is still in play. - _Ray Chandler_, Aug 05 2003 %Y A077712 Cf. A086981, A086982. %Y A077712 Subsequence of A005117. %K A077712 base,nonn %O A077712 1,2 %A A077712 _Amarnath Murthy_, Nov 19 2002 %E A077712 More terms from _Ray Chandler_, Aug 02 2003 %E A077712 Offset corrected by _Mohammed Yaseen_, Aug 16 2023