|
|
A089293
|
|
Sum of digits in the mixed-base enumeration system n=...d(4)d(3)d(2)d(1), where the digits satisfy 0<=d(i)<=1 if i is odd, 0<=d(i)<=2 if i is even.
|
|
1
|
|
|
0, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 3, 4, 4, 5, 5, 6, 4, 5, 5, 6, 6, 7, 1, 2, 2, 3, 3, 4, 2, 3, 3, 4, 4, 5, 2, 3, 3, 4, 4, 5, 3, 4, 4, 5, 5, 6, 3, 4, 4, 5, 5, 6, 4, 5, 5
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,4
|
|
COMMENTS
|
Counting 0,1,2,3,... (base 10) in this mixed-base system proceeds as follows: 0,1,10,11,20,21,100,101,110,111,120,121,1000,.. = A109827.
|
|
LINKS
|
|
|
FORMULA
|
a(n)=a(n-1)+1 if n=1, 3, 5 mod 6; a(n)=a(n-1) if n=2, 4 mod 5; a(n)=a(n/6) if n=0 mod 6.
|
|
EXAMPLE
|
11(base 10) = 121(mixed-base), so a(11)=4.
|
|
PROG
|
(PARI) a(n) = vecsum(digits(n, 6)\/2); \\ Kevin Ryde, Aug 03 2021
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,base,easy,less
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|