OFFSET
1,2
COMMENTS
Conjecture. The positive integers that are not in this sequence are given by the positions of 2 in the fixed-point of the morphism 0->01, 1->02, 2->03, 3->01 (see A191255). (This has been confirmed for over 5000 terms of A213257.) To illustrate, the fixed-point of the indicated morphism is {0,1,0,2,0,1,0,3,0,1,0,2,0,1,0,1,0,1,0,2,0,...} and 2 occurs at positions {4,12,20,...}, integers that are missing in A213257.
The positive integers that are not in this sequence are listed in A213258.
For the sequence containing no 3-term arithmetic progression,see A003278.
EXAMPLE
Given that the sequence begins {1, 2, 3, 5, 6, 7, 8, 9, 10, 11,...}, the next term, a(11), cannot be 12, because then the forbidden progression {3,6,12} would occur in the sequence. 13 is allowed, however, so a(11)=13.
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Jun 07 2012
STATUS
approved