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.

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

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

Table of n, a(n) for n=0..104.

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

Cf. A109827 (mixed-base).

Sums of digits in other bases: A000120 (binary), A053735 (ternary), A053827 (base 6).

Sequence in context: A299029 A200747 A328481 * A034968 A341513 A276150

Adjacent sequences: A089290 A089291 A089292 * A089294 A089295 A089296

Keyword

nonn,base,easy,less

Author

John W. Layman, Jan 15 2004

Status

approved