OFFSET
1,2
COMMENTS
At the (k+1)-th step of generating the Cantor set, the offsets from 1/4 to the center points of the deleted middle thirds are {a(i)/(4*(-3)^k) : 1 <= i <= 2^k}. Clearly, these offsets are negated for use with respect to 3/4.
Note that each quarter point of the Cantor ternary set, C, is also a quarter point of an interval-constrained subset of C that is an image of C scaled by 3^(-k) for all k >= 1.
If we replace -3m-4 and -3m+4 in the definition with -3m-2 and -3m+2 we get the terms of A191108 and their negation.
LINKS
Eric Weisstein's World of Mathematics, Cantor Set.
EXAMPLE
At the 2nd step of generating the Cantor set, the deleted middle thirds are (1/9, 2/9) and (7/9, 8/9) with center points 1/6 and 5/6. These points are offset from 1/4 by -1/12 and +7/12. The denominator for the 2nd step (i.e., k=1) is 4*(-3)^k = -12. So a(1) = -1 * -1 = 1 and a(2) = 7 * -1 = -7.
PROG
(PARI) A355680(size) = {a=vector(size); a[1] = 1;
forstep (n=2, size, 2, j=-3*a[n\2];
if(j>0, a[n-1]=j-4; a[n]=j+4, a[n-1]=j+4; a[n]=j-4);
print(n-1, " ", a[n-1]); print(n, " ", a[n]); ) }
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Peter Munn, Jul 14 2022
STATUS
approved