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 A202024 #15 Dec 24 2018 03:25:51
%S A202024 1,1,4,4,1,1,4,4,6,2,2,4,2,2,2,6,2,2,2,4,4,2,2,2,4,2,4,2,2,2,4,2,2,4,
%T A202024 2,2,2,4,2,2,2,4,2,2,2,4,2,2,2,2,4,2,2,2,4,2,2,2,2,2,4,2,2,2,4,2,2,2,
%U A202024 2,2,2,4,2,2,2,4,2,2,2,2,2,2,2,4,2,2,2
%N A202024 Lexicographically earliest positive integer sequence such that no sum of any number of consecutive terms is an integer of the form k^2+k+1 for any positive integer k.
%C A202024 After the first 16 terms, ending with ...,4,2,2,2,6, the sequence appears to consist entirely of 2's and 4's, with the spacing between successive 4's being 1,4,2,4,3,4,4,4,5,4,6,4,7,4,8,4,9,4,10,4,..., one bisection of which is 1,2,3,4,...,n,... This has been verified for the first 1000 terms.
%e A202024 Integers of the form k^2+k+1 for positive integer k are {3,7,13,21,...}. Assume that a(1)-a(3) have been determined as {1,1,4}. Then a(4)=1 gives consecutive terms 1,1,4,1 summing to 7, which is prohibited; a(4)=2 gives 1+4+2=7; a(4)=3 gives 4+3=7; but a(4)=4 is OK, giving no sum of consecutive terms equaling 3,7,13,... Thus a(4)=4.
%Y A202024 Cf. A168677.
%K A202024 nonn
%O A202024 1,3
%A A202024 _John W. Layman_, Dec 09 2011