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.

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, 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, 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

Offset

0,4

Comments

See A248625 for more information, links and examples.

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

Links

Sébastien Palcoux, Table of n, a(n) for n = 0..10000

Prog

(PARI) a=[]; for(n=1, 190, a=concat(a, 1); while(hasAP(a, 4), a[#a]++)); a \\ See A248625 for hasAP().
(SageMath)
cpdef FourFree(int n):
   cdef int i, r, k, s, L1, L2, L3
   cdef list L, Lb
   cdef set b
   L=[1, 1, 1]
   for k in range(3, n):
      b=set()
      for i in range(k):
         if 3*((k-i)/3)==k-i:
            r=(k-i)/3
            L1, L2, L3=L[i], L[i+r], L[i+2*r]
            s=3*(L2-L1)+L1
            if s>0 and L3==2*(L2-L1)+L1:
               b.add(s)
      if 1 not in b:
         L.append(1)
      else:
         Lb=list(b)
         Lb.sort()
         for t in Lb:
            if t+1 not in b:
               L.append(t+1)
               break
   return L
# Sébastien Palcoux, Aug 28 2019

Crossrefs

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

Sequence in context: A073203 A073204 A322286 * A282934 A273619 A327522

Adjacent sequences: A248638 A248639 A248640 * A248642 A248643 A248644

Keyword

nonn,easy

Author

M. F. Hasler, Oct 10 2014

Status

approved