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A355680
Numerator generator for offsets from the quarter points of the Cantor ternary set to the center points of deleted middle thirds: 1 is in the list and if m is in the list -3m-4 and -3m+4 are in the list, which is ordered by absolute value.
2
1, -7, 17, 25, -47, -55, -71, -79, 137, 145, 161, 169, 209, 217, 233, 241, -407, -415, -431, -439, -479, -487, -503, -511, -623, -631, -647, -655, -695, -703, -719, -727, 1217, 1225, 1241, 1249, 1289, 1297, 1313, 1321, 1433, 1441, 1457, 1465, 1505, 1513, 1529, 1537, 1865
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
Essentially, the positions of isolated 0's in A355682.
Cf. A191108.
Sequence in context: A309231 A183897 A300186 * A354672 A261934 A253075
KEYWORD
sign,easy
AUTHOR
Peter Munn, Jul 14 2022
STATUS
approved