OFFSET
1,1
COMMENTS
Conjecture. The terms of 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 in this sequence but missing from A213257.
It appears that the terms of this sequence are all of the form of 4 times an odd integer multiplied by a nonnegative power of 8.
The above two conjectures are correct. This is indeed positions of 2 in A191255, and numbers of the form 2^(3t+2)*s where s is an odd number. - Jianing Song, Sep 21 2018
The asymptotic density of this sequence is 1/7. - Amiram Eldar, May 31 2024
FORMULA
MATHEMATICA
Select[Range[500], Mod[IntegerExponent[#, 2], 3] == 2 &] (* Amiram Eldar, May 31 2024 *)
PROG
(PARI) is(n) = valuation(n, 2) % 3 == 2; \\ Amiram Eldar, May 31 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
John W. Layman, Jun 07 2012
STATUS
approved