A398006 a(n) is the sum of digits in the canonical snowball representation of n.

0, 1, 1, 2, 1, 3, 2, 2, 1, 3, 3, 4, 2, 2, 2, 4, 1, 5, 3, 3, 3, 3, 4, 6, 2, 2, 2, 4, 2, 4, 4, 4, 1, 5, 5, 5, 3, 3, 3, 3, 3, 6, 3, 3, 4, 5, 6, 7, 2, 2, 2, 6, 2, 4, 4, 4, 2, 4, 4, 6, 4, 4, 4, 4, 1, 7, 5, 5, 5, 7, 5, 8, 3, 3, 3, 3, 3, 5, 3, 3, 3, 5, 6, 5, 3, 3, 3

Offset

0,4

Comments

See A397794 for the definition of the canonical snowball representation of a number.

Links

Rémy Sigrist, Table of n, a(n) for n = 0..8192

Formula

a(2*n) = a(n).

a(n) = 1 iff n is a power of 2.

a(A200748(n)) = n (and this is the first occurrence of n in the sequence).

Example

The first terms are:
  n   a(n)  snowball(n)
  --  ----  -----------
   0     0            0
   1     1            1
   2     1           10
   3     2           11
   4     1          100
   5     3           21
   6     2          110
   7     2          101
   8     1         1000
   9     3          111
  10     3          210
  11     4          121
  12     2         1100
  13     2         1001
  14     2         1010
  15     4          211
  16     1        10000

Prog

(PARI) a(n) = { my (b = 2, s = 0, d); while (n, d = n % b; n \= b; s += d; b = 2+d; ); return (s); }

Crossrefs

Cf. A034968, A200748, A397794.

Sequence in context: A126303 A306467 A157810 * A072339 A342507 A261337

Adjacent sequences: A398000 A398001 A398002 * A398008 A398009 A398010

Keyword

nonn,base,new

Author

Rémy Sigrist, Jul 17 2026

Status

approved