cp's OEIS Frontend

A065447 Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).

%I A065447 #32 Mar 09 2024 11:12:33
%S A065447 1,100,100111,1001110000,100111000011111,100111000011111000000,
%T A065447 1001110000111110000001111111,100111000011111000000111111100000000,
%U A065447 100111000011111000000111111100000000111111111,1001110000111110000001111111000000001111111110000000000
%N A065447 Concatenation of 1, 00, 111, 0000, ..., n 1's (if n is odd) or n 0's (if n is even).
%C A065447 a(n) is divisible by A002275([(n+1)/2]) = (10^[(n+1)/2]-1)/9. Cf. A262806. - _Max Alekseyev_, Jun 02 2013
%C A065447 The unique sequence of binary words a(n) such that the k-th run of a(n) has length k, for k = 1..n . - _Clark Kimberling_, Mar 08 2024
%H A065447 Harry J. Smith, <a href="/A065447/b065447.txt">Table of n, a(n) for n = 1..44</a>
%e A065447 a(2) = 100, the concatenation of one 1, two 0's.
%e A065447 a(3) = 100111, the concatenation of one 1, two 0's, three 1's.
%e A065447 a(4) = 1001110000, the concatenation of one 1, two 0's, three 1's, four 0's.
%p A065447 a:= n-> parse(cat((irem(i,2)$i)$i=1..n)):
%p A065447 seq(a(n), n=1..10);  # _Alois P. Heinz_, Mar 08 2024
%t A065447 FoldList[Join, {1}, Map[ConstantArray[Mod[#, 2], #] &, Range[2, 10]]] (* _Peter J. C. Moses_, Mar 08 2024 *)
%o A065447 (PARI) { m=10; for (n=1, 44, if (n==1, a=1, m*=10; a*=m; if (n%2, a+=(m - 1)/9)); write("b065447.txt", n, " ", a) ) } \\ _Harry J. Smith_, Oct 19 2009
%Y A065447 For decimal version see A065760.
%Y A065447 Cf. A000217, A065761, A371032.
%K A065447 base,easy,nonn
%O A065447 1,2
%A A065447 _Lior Manor_, Nov 18 2001