OFFSET
1,2
COMMENTS
See discussions at A190803, A191106. The sequence a=A191108 has closure properties: the positive integers in (2+A191108)/3 comprise A191108, as do those in (-2+A191108)/3.
From Peter Munn, May 13 2019: (Start)
The closure of {1} in the positive integers under reflection about 3^k, k >= 1.
Asymptotic density is 0.
Consider a Sierpinski arrowhead curve formed of edges numbered consecutively from 0 at its axis of symmetry. The m-th edge is contained in the boundary of the plane sector occupied by the arrowhead if and only if m or -m is in this sequence.
For k >= 0, a(2^k) = 2*3^k - 1 and {a(i)/(2*3^k) | 1 <= i <= 2^k} is the set of center points of surviving intervals at the k-th step of generating the Cantor set, and therefore the set of center points of deleted middle-third intervals at the (k+1)-th step.
Define t: Z -> P(R) so that t(n) is the translated Cantor ternary set spanning [(n-1)/2, (n+1)/2], and let T be the union of t(a(n)) for all n. T = T * 3 = T / 3 is the closure of the Cantor ternary set under multiplication by 3.
(End)
LINKS
Ivan Neretin, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Cantor Set
Wikipedia, SierpiĆski arrowhead curve
FORMULA
MATHEMATICA
PROG
(PARI) a(n) = fromdigits(binary(n-1), 3)<<2 + 1; \\ Kevin Ryde, Aug 05 2022
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Clark Kimberling, May 26 2011
STATUS
approved