A181611 Position of rightmost zero in 2^n (including leading zero).

1, 1, 1, 2, 2, 2, 3, 3, 3, 2, 2, 2, 4, 5, 5, 5, 2, 6, 6, 5, 5, 1, 1, 8, 8, 4, 9, 9, 3, 8, 10, 10, 10, 11, 11, 11, 12, 4, 12, 11, 8, 1, 1, 5, 5, 12, 12, 3, 15, 7, 16, 3, 3, 7, 8, 8, 8, 12, 7, 7, 10, 1, 1, 7, 4, 4, 21, 13, 7, 4, 4, 22, 6, 6, 4, 23, 24, 13, 2, 4, 25, 1, 1, 11, 6, 26, 3, 2, 12, 12, 12, 11, 14, 14, 23, 3, 3, 4, 4, 4, 3, 1, 1, 2, 2, 2, 6, 6, 8, 2, 2, 2, 3, 3, 3, 17, 2, 5, 6, 6, 6

Offset: 1

Author

Tanya Khovanova, Jan 30 2011

Keywords

• nonn
• base

Comments

"Positions" are counted 0,1,2,3,... starting with the least significant digit.

Examples

			2^10 = 1024, the rightmost zero is in position 2, so a(10) = 2. Another example, 2^5 = 32, so we need to add a leading zero: 032, thus the rightmost zero will be in position 2, and a(5) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A031142, A031141.

Cf. A000079, A215887.

Programs

Maple

A181611 := proc(n) local dgs,i ; dgs := convert(2^n, base, 10) ; i := ListTools[Search](0, dgs) ; if i > 0 then i-1; else nops(dgs) ; end if ; end proc: # R. J. Mathar, Jan 30 2011
a:= proc(n) local m, i;
      m:= 2^n;
      for i from 0 while m>0 and irem(m, 10, 'm')<>0
      do od; i
    end:
seq(a(n), n=1..121);  # Alois P. Heinz, Feb 05 2011

Mathematica

Table[Position[Reverse[Prepend[IntegerDigits[2^n], 0]],
    0][[1]][[1]] - 1, {n, 121}]

PARI

a(n) = {my(d = Vecrev(digits(2^n))); for (i=1, #d, if (!d[i], return (i-1));); #d;} \\ Michel Marcus, Jan 01 2016

Formula

a(n) = A215887(A000079(n)). - Michel Marcus, Jan 01 2016