A259143 Number of distinct digits needed to write the calendar date of n-th day of a non-leap year in decimal representation, without leading zeros.
1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 3, 2, 2, 3, 3, 3, 3, 3, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 3, 3, 3, 3
Offset: 1
Examples
. | Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec
. | 1 2 3 4 5 6 7 8 9 10 11 12
. ----+-------------------------------------------------
. 1 | 1 2 2 2 2 2 2 2 2 2 1 2
. 2 | 2 1 2 2 2 2 2 2 2 3 2 2
. 3 | 2 2 1 2 2 2 2 2 2 3 2 3
. 4 | 2 2 2 1 2 2 2 2 2 3 2 3
. 5 | 2 2 2 2 1 2 2 2 2 3 2 3
. 6 | 2 2 2 2 2 1 2 2 2 3 2 3
. 7 | 2 2 2 2 2 2 1 2 2 3 2 3
. 8 | 2 2 2 2 2 2 2 1 2 3 2 3
. 9 | 2 2 2 2 2 2 2 2 1 3 2 3
. 10 | 2 3 3 3 3 3 3 3 3 2 2 3
. 11 | 1 2 2 2 2 2 2 2 2 2 1 2
. 12 | 2 2 3 3 3 3 3 3 3 3 2 2
. 13 | 2 3 2 3 3 3 3 3 3 3 2 3
. 14 | 2 3 3 2 3 3 3 3 3 3 2 3
. 15 | 2 3 3 3 2 3 3 3 3 3 2 3
. 16 | 2 3 3 3 3 2 3 3 3 3 2 3
. 17 | 2 3 3 3 3 3 2 3 3 3 2 3
. 18 | 2 3 3 3 3 3 3 2 3 3 2 3
. 19 | 2 3 3 3 3 3 3 3 2 3 2 3
. 20 | 3 2 3 3 3 3 3 3 3 3 3 3
. 21 | 2 2 3 3 3 3 3 3 3 3 2 2
. 22 | 2 1 2 2 2 2 2 2 2 3 2 2
. 23 | 3 2 2 3 3 3 3 3 3 4 3 3
. 24 | 3 2 3 2 3 3 3 3 3 4 3 3
. 25 | 3 2 3 3 2 3 3 3 3 4 3 3
. 26 | 3 2 3 3 3 2 3 3 3 4 3 3
. 27 | 3 2 3 3 3 3 2 3 3 4 3 3
. 28 | 3 2 3 3 3 3 3 2 3 4 3 3
. 29 | 3 _ 3 3 3 3 3 3 2 4 3 3
. 30 | 3 _ 2 3 3 3 3 3 3 3 3 4
. 31 | 2 _ 2 _ 3 _ 3 3 _ 3 _ 3 .
13 days need just 1 digit: {1, 11, 33, 53, 62, 94, 125, 157, 188, 220, 252, 305, 315} = {Jan 1, Jan 11, Feb 2, Feb 22, Mar 3, Apr 4, May 5, Jun 6, Jul 7, Aug 8, Sep 9, Nov 1, Nov 11};
152 days need 2 digits: the first is the 2nd day = Jan 2, the last one is the 356th day = Dec 22;
192 days need 3 digits: the first is the 20th day = Jan 20, the last one is the last day of the year = Dec 31;
8 days need 4 digits: {296 .. 302, 364} = Oct 23 through Oct 29, and also the penultimate day of the year = Dec 30.
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..365
- Wikipedia, Calendar date
- Index entries for sequences related to calendars
Crossrefs
Cf. A008685.
Programs
-
Haskell
import Data.List (nub) a259143 n = a259143_list !! (n-1) a259143_list = [length $ nub $ show m ++ show d | m <- [1 .. 12], d <- [1 .. a008685 m]]
Comments