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

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..20000

Michael Gilleland, Some Self-Similar Integer Sequences

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 ]

Crossrefs

Sequence in context: A120562 A178692 A364144 * A281511 A249337 A316848

Adjacent sequences: A033663 A033664 A033665 * A033667 A033668 A033669

Keyword

nonn,base

Author

David W. Wilson, Wouter Meeussen

Status

approved