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 A248641 #29 Aug 28 2019 12:52:51 %S A248641 1,1,1,2,1,1,2,1,1,1,2,2,2,3,1,1,1,2,1,2,2,2,3,3,3,1,1,3,1,1,1,2,2,1, %T A248641 2,2,1,2,2,2,3,3,2,3,2,3,3,5,1,1,1,3,1,1,3,1,1,1,2,2,2,3,1,2,1,1,1,2, %U A248641 2,2,3,4,2,3,2,2,2,3,3,1,3,3,3,5,5,4,1,1,1,3,1,2,3,1,5,3,2,6,1,3,2,2,3,2,1,1,3,3,1,1,1 %N A248641 Lexicographically earliest positive sequence which does not contain a 4-term equidistant subsequence (a(n+k*d); k=0,1,2,3) in arithmetic progression. %C A248641 See A248625 for more information, links and examples. %C A248641 It is a variation of A229037 where 3-term is replaced by 4-term (and with “lead index” 0 instead of 1) %H A248641 Sébastien Palcoux, <a href="/A248641/b248641.txt">Table of n, a(n) for n = 0..10000</a> %o A248641 (PARI) a=[];for(n=1,190,a=concat(a,1);while(hasAP(a,4),a[#a]++));a \\ See A248625 for hasAP(). %o A248641 (SageMath) %o A248641 cpdef FourFree(int n): %o A248641 cdef int i, r, k, s, L1, L2, L3 %o A248641 cdef list L, Lb %o A248641 cdef set b %o A248641 L=[1, 1, 1] %o A248641 for k in range(3, n): %o A248641 b=set() %o A248641 for i in range(k): %o A248641 if 3*((k-i)/3)==k-i: %o A248641 r=(k-i)/3 %o A248641 L1, L2, L3=L[i], L[i+r], L[i+2*r] %o A248641 s=3*(L2-L1)+L1 %o A248641 if s>0 and L3==2*(L2-L1)+L1: %o A248641 b.add(s) %o A248641 if 1 not in b: %o A248641 L.append(1) %o A248641 else: %o A248641 Lb=list(b) %o A248641 Lb.sort() %o A248641 for t in Lb: %o A248641 if t+1 not in b: %o A248641 L.append(t+1) %o A248641 break %o A248641 return L %o A248641 # _Sébastien Palcoux_, Aug 28 2019 %Y A248641 Cf. A248625, A248639, A248640, A248627, A229037, A241752. %K A248641 nonn,easy %O A248641 0,4 %A A248641 _M. F. Hasler_, Oct 10 2014