A248641 - OEIS

%I #29 Aug 28 2019 12:52:51

%S 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 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 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 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 See A248625 for more information, links and examples.

%C It is a variation of A229037 where 3-term is replaced by 4-term (and with “lead index” 0 instead of 1)

%H Sébastien Palcoux, <a href="/A248641/b248641.txt">Table of n, a(n) for n = 0..10000</a>

%o (PARI) a=[];for(n=1,190,a=concat(a,1);while(hasAP(a,4),a[#a]++));a \\ See A248625 for hasAP().

%o (SageMath)

%o cpdef FourFree(int n):

%o    cdef int i, r, k, s, L1, L2, L3

%o    cdef list L, Lb

%o    cdef set b

%o    L=[1, 1, 1]

%o    for k in range(3, n):

%o       b=set()

%o       for i in range(k):

%o          if 3*((k-i)/3)==k-i:

%o             r=(k-i)/3

%o             L1, L2, L3=L[i], L[i+r], L[i+2*r]

%o             s=3*(L2-L1)+L1

%o             if s>0 and L3==2*(L2-L1)+L1:

%o                b.add(s)

%o       if 1 not in b:

%o          L.append(1)

%o       else:

%o          Lb=list(b)

%o          Lb.sort()

%o          for t in Lb:

%o             if t+1 not in b:

%o                L.append(t+1)

%o                break

%o    return L

%o # _Sébastien Palcoux_, Aug 28 2019

%Y Cf. A248625, A248639, A248640, A248627, A229037, A241752.

%K nonn,easy

%O 0,4

%A _M. F. Hasler_, Oct 10 2014