A248640 -id:A248640 - cp's OEIS frontend

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

M. F. Hasler, Oct 10 2014

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)

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

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

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

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

A248639 Least nonnegative sequence which does not contain a 4-term equidistant subsequence (a(n+k*d); k=0,1,2,3) in arithmetic progression.

Original entry on oeis.org

0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 1, 1, 2, 0, 0, 0, 1, 0, 1, 1, 1, 2, 2, 2, 0, 0, 2, 0, 0, 0, 1, 1, 0, 1, 1, 0, 1, 1, 1, 2, 2, 1, 2, 1, 2, 2, 4, 0, 0, 0, 2, 0, 0, 2, 0, 0, 0, 1, 1, 1, 2, 0, 1, 0, 0, 0, 1, 1, 1, 2, 3, 1, 2, 1, 1, 1, 2, 2, 0, 2, 2, 2, 4, 4, 3, 0, 0, 0, 2, 0, 1, 2, 0, 4, 2, 1, 5, 0, 2, 1, 1, 2, 1, 0, 0, 2, 2, 0, 0, 0, 3, 0, 0, 1, 1, 1, 4, 1, 2, 3, 0, 1, 2, 1, 0, 3, 3, 4, 1, 1, 3

Offset: 0

M. F. Hasler, Oct 10 2014

nonn

See A248625 for more information, links and examples.

See A248641 for the "positive integers" variant.

Cf. A248625, A248640, A248641, A248627, A229037, A241752.

a=[];for(n=1,190,a=concat(a,0);while(hasAP(a,4),a[#a]++));a \\ See A248625 for hasAP().

cp's OEIS Frontend

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.

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