In Excel, how to fill down consecutive integers following a pattern 1, 1, 2, 2,

I don't think Excel includes the logic to do this, although I'll be happy to be proved wrong.

A workaround would be to use a formula copied down the column, then use PasteSpecial>Values to overwrite with the desired values.

   A       B        C
1  1
2  1
3  =A1+1
4  =A2+1
5  =A3+1

etc.

No Excel here, but in OpenOffice.org, filling down the following value and formula:

      A
1     1
2   =A1

...gets me new values and formulas:

      A
1     1
2   =A1
3     2
4   =A3
5     3
6   =A5
7     4
8   =A7

...which displays as you want it to.

For a pure formula version,

=ROUNDUP(ROW(A1)/2,0) will fill down correctly. (If starting further down than row 1, subtract as needed.)