cp's OEIS Frontend

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.

%I A355680 #10 Feb 16 2025 08:34:03
%S A355680 1,-7,17,25,-47,-55,-71,-79,137,145,161,169,209,217,233,241,-407,-415,
%T A355680 -431,-439,-479,-487,-503,-511,-623,-631,-647,-655,-695,-703,-719,
%U A355680 -727,1217,1225,1241,1249,1289,1297,1313,1321,1433,1441,1457,1465,1505,1513,1529,1537,1865
%N 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.
%C A355680 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.
%C A355680 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.
%C A355680 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.
%H A355680 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/CantorSet.html">Cantor Set</a>.
%e A355680 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.
%o A355680 (PARI) A355680(size) = {a=vector(size); a[1] = 1;
%o A355680 forstep (n=2,size,2, j=-3*a[n\2];
%o A355680   if(j>0, a[n-1]=j-4;a[n]=j+4, a[n-1]=j+4;a[n]=j-4);
%o A355680   print(n-1," ",a[n-1]); print(n," ",a[n]);) }
%Y A355680 Essentially, the positions of isolated 0's in A355682.
%Y A355680 Cf. A191108.
%K A355680 sign,easy
%O A355680 1,2
%A A355680 _Peter Munn_, Jul 14 2022