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 A268129 #7 Jan 27 2016 12:22:48
%S A268129 1,2,3,5,4,6,10,7,8,9,17,11,12,23,13,14,15,29,16,18,34,19,20,21,41,22,
%T A268129 24,46,25,26,27,53,28,30,58,31,32,33,65,35,36,71,37,38,39,77,40,42,82,
%U A268129 43,44,45,89,47,48,95,49,50,51,101,52,54,106,55,56,57,113,59,60,119,61,62,63,125,64,66,130,67,68,69,137,70,72,142,73,74,75
%N A268129 If a(n) is a multiple of 3, then a(n+1) = a(n) + a(n-1). Lexicographic first permutation of the positive integers with this property.
%C A268129 A variant of the sequence A267758 where the relation has to hold for prime numbers rather than for multiples of 3. In contrast to that sequence we only have two "bands" or lines here. L. Blomberg has studies several properties of this sequence (private communication).
%H A268129 M. F. Hasler, <a href="/A268129/b268129.txt">Table of n, a(n) for n = 1..1000</a>
%H A268129 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o A268129 (PARI) {a(n,show=1,a=[1],L=0/*up to L all numbers are used*/,U=[]/*numbers > L already used*/)=while(#a<n,show&&print1(a[#a]",");/*if the last term is larger than L+1, add it to U*/ if(a[#a]>L+1,U=setunion(U,[a[#a]]),/*else increase L and remove terms from U if possible*/ L++;while(#U&&U[1]<=L+1,U=U[^1];L++));a=concat(a,if(a[#a]%3,L+1,a[#a]+a[#a-1])));a}
%K A268129 nonn
%O A268129 1,2
%A A268129 _Eric Angelini_, _Lars Blomberg_ and _M. F. Hasler_, Jan 26 2016