A117407 - OEIS

%I #4 Mar 31 2012 10:31:13

%S 1,2,1,3,4,5,2,6,7,3,8,9,10,4,11,12,13,5,14,15,6,16,17,18,7,19,20,8,

%T 21,22,23,9,24,25,26,10,27,28,11,29,30,31,12,32,33,34,13,35,36,14,37,

%U 38,39,15,40,41,16,42,43,44,17,45,46,47,18,48,49,19,50,51,52,20,53,54,21,55

%N a(n) = j if n is T(j), else a(n) = k if n is U(k), where T is a Beatty sequence based on (sqrt(5)+5)/2 (A054770) and U is its complement (A063732).

%C Every positive integer occurs exactly twice. Taking a Lucas number (A000032) of terms L(n) starting at a(0), the last two terms are a pair of Fibonacci numbers (A000045). If n is even, then the last two terms are F(n+1) followed by F(n-1), if n is odd they are F(n-1) followed by F(n+1), where F is the Fibonacci sequence. For example, the first L(4) = 7 terms of this sequence are (1,2,1,3,4,5,2) and the last members are 5 and 2 which are equal to F(5) and F(3). Note also that L(n) = F(n-1) + F(n+1).

%e a(9) = 3 because 9 = T(3).

%Y Cf. A026272, A026242.

%K nonn

%O 0,2

%A _Casey Mongoven_, Mar 13 2006