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

Author

Henry Bottomley, Feb 14 2001

Keywords

• base
• nonn

Examples

			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).
		

Links

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

Crossrefs

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

Programs

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

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 *)