A059941 Take the n-th number which is just a sequence of 1's and 2's (A007931): if the first k digits in order are the same as the last k digits in order then put 1 in the k-th from right digit of a(n), otherwise put a zero.

1, 1, 11, 10, 10, 11, 111, 100, 101, 100, 100, 101, 100, 111, 1111, 1000, 1001, 1000, 1001, 1010, 1001, 1000, 1000, 1001, 1010, 1001, 1000, 1001, 1000, 1111, 11111, 10000, 10001, 10000, 10011, 10000, 10001, 10000, 10001, 10010, 10101, 10000

Offset

1,3

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Example

a(35)=10011 since the 35th number with 1's and 2's is 11211, the first digit and last digit are the same (1), the first two and the last two are the same (11), the first three and last three are not (112 and 211), the first four and last four are not (1121 and 1211) and the first five and last five are (11211).

Mathematica

a[n_] := (id = Drop[ IntegerDigits[n+1, 2], 1] + 1; an = {}; Do[ PrependTo[an, If[Take[id, k] == Take[id, -k], 1, 0]], {k, 1, Length[id]}]; FromDigits[an]); Table[a[n], {n, 1, 42}](* Jean-François Alcover, Nov 21 2011 *)

Prog

(Haskell)
import Data.List (inits, tails)
a059941 n = a059941_list !! (n-1)
a059941_list = map (foldr (\d v -> v * 10 + d) 0) $ f a030341_tabf where
   f (xs:xss)
     | 0 `elem` xs = f xss
     | otherwise = map fromEnum (zipWith (==)
                   (tail $ inits xs) (reverse $ init $ tails xs)) : f xss
-- Reinhard Zumkeller, Apr 03 2014

Crossrefs

A059942 is this sequence translated from binary to decimal. Cf. A007931, A059943.

Sequence in context: A112952 A343959 A070561 * A086100 A182782 A217789

Adjacent sequences: A059938 A059939 A059940 * A059942 A059943 A059944

Keyword

base,nonn

Author

Henry Bottomley, Feb 14 2001

Status

approved