A033666 Base-2 digital convolution sequence (with smallest digits).

1, 1, 1, 2, 1, 2, 2, 3, 1, 3, 2, 4, 2, 4, 3, 5, 1, 2, 3, 4, 2, 3, 4, 5, 2, 3, 4, 5, 3, 4, 5, 6, 1, 3, 2, 4, 3, 5, 4, 6, 2, 4, 3, 5, 4, 6, 5, 7, 2, 4, 3, 5, 4, 6, 5, 7, 3, 5, 4, 6, 5, 7, 6, 8, 1, 3, 3, 5, 2, 4, 4, 6, 3, 5, 5, 7, 4, 6, 6, 8, 2, 4, 4, 6, 3, 5, 5, 7, 4, 6, 6, 8, 5, 7, 7, 9, 2, 4, 4, 6, 3, 5

Offset: 0

Author

David W. Wilson, Wouter Meeussen

Keywords

• nonn
• base

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..20000
• Michael Gilleland, Some Self-Similar Integer Sequences

Programs

Maple

a:= proc(n) option remember; `if`(n=0, 1, (l->
      add(l[-i]*a(i-1), i=1..nops(l)))(Bits[Split](n)))
    end:
seq(a(n), n=0..101);  # Alois P. Heinz, Apr 14 2021

Mathematica

c[ 0,  ] := 1; c[ n, b_ ] := c[ n, b ]=Module[ {mul}, mul=IntegerDigits[ n, b ]; Table[ c[ i, b ], {i, 0, Length[ mul ]-1} ].mul ]