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 A268131 #7 Jan 27 2016 12:23:03
%S A268131 1,2,3,4,7,5,6,8,14,9,23,10,11,12,23,13,15,16,31,17,18,35,19,20,39,21,
%T A268131 22,24,46,25,71,26,27,53,28,81,109,29,30,32,62,33,34,36,70,37,38,40,
%U A268131 78,41,42,43,44,87,45,132,177,47,48,95,49,144,193,50,243
%N A268131 If a(n) is not squarefree, then a(n+1) = a(n) + a(n-1), else a(n+1) is the smallest positive integer not occurring earlier.
%C A268131 A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for squarefree numbers. In contrast to that sequence we have many "lines" here (when the property occurs for consecutive terms), roughly proportional to n, 2n, 3n, ... Here we also have duplicate terms (which we could exclude explicitly), for n <= 1000 this happens 19 times.
%H A268131 M. F. Hasler, <a href="/A268131/b268131.txt">Table of n, a(n) for n = 1..1000</a>
%o A268131 (PARI) {a(n,show=0,is=x->issquarefree(x),a=[1],L=0,U=[])->while(#a<n,show&&if(type(show)=="t_STR",write(show,#a," ",a[#a]),print1(a[#a]","));if(a[#a]>L+1,U=setunion(U,[a[#a]]),L++;while(#U&&U[1]<=L+1,U=U[^1];L++));a=concat(a,if(is(a[#a]),L+1,a[#a]+a[#a-1])));if(type(show)=="t_VEC",a,a[#a])}
%K A268131 nonn,look
%O A268131 1,2
%A A268131 _M. F. Hasler_, Jan 26 2016