|
|
A333355
|
|
Number of bits in binary expansion of n minus the number of digits of n when written in base 3.
|
|
0
|
|
|
0, 1, 0, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,8
|
|
COMMENTS
|
Record highs are at n = 2^A054414. All n=2^k >= 2 are increases, all n=3^j are decreases, and there is either one or none 3^j between 2^(k-1) and 2^k. When one, a(2^k) = a(2^(k-1)) so not a record high. When none, a(2^k) = a(2^(k-1)) + 1 which is a record high. If 2^k and 2^(k-1) are the same length in ternary then there is no 3^j between them. This is when 2^k has most significant ternary digit 2 since 2^(k-1) >= 3^j is 2^k >= 2*3^j. These k are A054414. Non-record increases are at its complement n = 2^A020914 >= 2. - Kevin Ryde, Apr 04 2020
|
|
LINKS
|
|
|
FORMULA
|
|
|
EXAMPLE
|
a(8) = 2 = 4 - 2 for binary 1000 and ternary 22.
a(64) = 3 = 7 - 4 for binary 1000000 and ternary 2101.
|
|
MAPLE
|
a:= n-> ilog[2](n)-ilog[3](n):
|
|
MATHEMATICA
|
a[n_]: = Floor @ Log[2, n] - Floor @ Log[3, n]; Array[a, 100] (* Amiram Eldar, Mar 16 2020 *)
|
|
PROG
|
(Rexx)
L = 1 ; M = 1 ; B = 2 ; T = 3 ; S = 0
do N = 2 while length( S ) < 258
if B = N then do ; B = B * 2 ; L = L + 1 ; end
if T = N then do ; T = T * 3 ; M = M + 1 ; end
S = S || ', ' L - M
end N
say S ; return S
(PARI) a(n) = logint(n, 2) - logint(n, 3); \\ Kevin Ryde, May 15 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|