OFFSET
1,1
COMMENTS
These numbers correspond to the 1's in the (3/2)-expansion of 1/2, as defined by Renyi.
LINKS
W. Parry, On the beta-Expansions of Real Numbers, Acta Math. Acad. Sci. Hungar. 11, 401-416, 1960.
A. Renyi, Representations for real numbers and their ergodic properties, Acta Math. Acad. Sci. Hung. 8 (1957) 477-493.
FORMULA
a(n) = A077468(n+1) - 1. - Andrey Zabolotskiy, Nov 03 2024
EXAMPLE
The first power of 2/3 that is smaller than 1/2 is (2/3)^2, so the first term of the sequence is 2. Subtracting (2/3)^2 from 1/2 leaves 1/18. The first power of 2/3 that is less than 1/18 is (2/3)^8, so the next term of the sequence is 8.
MAPLE
x:= 1/2:
for i from 1 to 100 do
A[i]:= ceil(log[2/3](x));
x:= x-(2/3)^A[i];
od:
seq(A[i], i=1..100); # Robert Israel, Feb 15 2023
MATHEMATICA
PositionIndex[RealDigits[1/2, 3/2, 100, -1][[1]]][[2]]
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
James Propp, Feb 15 2023
STATUS
approved